Class 6 Maths - Ratio and Proportion Extra Questions

Answer

9 : 10

Q2) The ratio of the number of soccer balls to that of basketballs in a storeroom was 2 : 3. When another 144 balls were put into the storeroom, there were twice as many soccer balls and thrice as many basketballs. How many soccer balls and basketballs were there in the storeroom originally?

Answer

90 balls

Q3) The ratio of Sammy's age to Peter's age is 10 : 7. In 8 years' time, the ratio will become 4 : 3. What is Sammy's age now?

Ans: _____________
Answer
40

Q4) The ratio of the mass of chicken to the mass of fish was 3 : 5.
16 kg of fish was sold to the customers. After that, the ratio of the mass of chicken to the mass of fish was 7 : 9. Find the mass of the fish at first.

Ans: _____________
Answer
70 kg

Q5) Given the model below, find the ratio of A to B. Express your ratio in its simplest form.

Ans: ______________

Answer
3 : 2

Q6) Kenny jogged from point A to point B to point C along Greenside Park. The ratio of the distance of AB to AC is 9 : 14. Find the distance that Kenny jogged from point A to point C.

Ans: ____________m

Answer

5040

Q7) Ali has six times as many marbles as Norman. The ratio of the number of Norman's marbles to the number of Ray's marbles is 5 : 3. Find the ratio of the number of Ali's marbles to the number of Ray's marbles.

Ans: _______________

Answer

10 : 1

Q8) What is the ratio of the length of the toothbrush to the length of the pencil?



Ans: ____________

Answer

4 : 3

Q9) Catherine, Mindy and Shawn shared some beads in the ratio 3 : 4 : 5 respectively.
During a game, Mindy lost 13​  of her beads to Catherine and won 25​  of Shawn's.

a) What is the ratio of Mindy's beads to Shawn's beads now?
b) How many beads does Catherine have now if they have a total of 252 beads?

Ans: (a) ____________

         (b) ____________
Answer
a) 14 : 9
b) 91

Q10) The figure below is made up of a square and a rectangle.
The ratio of the shaded area to the unshaded area of the square is 5 : 11.
The ratio of the shaded area to the unshaded area of the rectangle is 3 : 4.


a) What is the shaded area of the square?
b) What is the breadth of the rectangle?

Ans: (a) ______________ (b) ______________

Answer
a) 45cm2
b) 7.5cm

Q11) There are 2 700 books in a school library. The number of Sanskrit, Hindi and English books is in the ratio of 5 : 3 : 7 respectively. When 504 new books are added, the number of Sanskrit books increased by 12% and the number of English books increased by 25%.

a) What is the total number of new Sanskrit and English books?

b) What is the percentage increase in the number of Hindi books?

Ans: (a) _____________

        (b) _____________
Answer
a) 423
b) 15%

Q12) Mr Seth wants to buy a plasma television. The selling price of the plasma television is $5 000. A discount of 8% is given is Mr Seth pays in cash. If he wishes to pay by installments, there will be no discount but he has to pay a 10% down payment and monthly installments of $400 for 12 months. How much will Mr Seth save if he pays in cash instead of paying by installments?
Ans:________________ 
Answer
$700

Q13) 46% of the books in a bookshop are English books. The rest are Sanskrit and Hindi books. The ratio of the number of Sanskrit books to the number of Hindi books is 2 : 7. There are 90 more English books than Hindi books.
(a) What percentage of the books are Hindi books?
 (b) How many books are there altogether?

Ans: (a)______________ 
         (b)______________ 
Answer
a) 42%
 b) 2250 books

Q14) The teacher-to-pupil ratio for an excursion was 3:16.
The number of girls was 7/9​  of the number of boys.
There are 72 boys who had gone to the excursion.

How many teachers were there?


Ans: ________________

Answer

24 teachers

Q15) Wei Jie ate 4 chocolates and 10 sweets. Min Han ate 6 chocolates and 6 sweets. What is the ratio of the total number of sweets to the total number of chocolates that were eaten by the 2 boys? Give your answer in the simplest form.



Ans:______________________
Answer
8 : 5

Q16) The ratio of Alan's total marks to that of Benji's total marks in their Mid-Year Examinations was 4 : 5. Alan's marks increased by 50% in the End-of-Year Examinations. By what percentrage must Benji's marks be increased so that their total marks would be equal?

Ans:________________ 

Answer
20%

Q17) The ratio of the number of papayas to the number of mangoes in Box A and in Box B are 2 : 1 and 2 : 7 respectively. Box A has  2/3 times as many fruit as Box B.

(a) Find the ratio of the number of papayas in Box A to the number of papayas in Box B.
(b) When 18 mangoes are moved from Box B to Box A, the ratio of the number of papayas to the number of mangoes in Box A becomes 8 : 7. How many mangoes are there in Box A now?



Ans:

(a) _____________________
(b)______________________

Answer
a) 2 : 1
b) 42 mangoes

Q18) There are 4 times as many apples as pears. If the ratio of the number of oranges to the number of pears is 2 : 3, what is the ratio of the number of oranges to the number of pears to the number of apples?


Ans:___________________

Answer
2 : 3 : 12

Q19) Marcus, Larry and Joe shared some stickers. On average, each boy had 42 stickers. After each boy bought another 20 stickers, the ratio of Marcus's stickers to Larry's to Joe's is 2 : 1 : 3. How many stickers did Larry have now?

Ans:______________ 

Answer

31 stickers

Q20) The ratio of Jiawen's savings to Bobby's savings is 1 : 5. The ratio of Bobby's savings to Lily's savings is 3 : 2. How much is their total savings if Jiawen saves $35 less than Lily?

Ans:__________________ 
Answer
$140

Q21) Michael bought some apples and gave half of them to Jackson.
Jackson bought some pears and gave half of them to Michael.
Michael threw away 25 pears that were rotten while Jackson bought for himself another 20 apples. After that, the number of pears to apples Michael had were in the ratio of 1 : 4 and the number of pears to apples Jackson had were in the ratio of 1 : 2. How many pears did Jackson buy?

Ans: _______________
Answer
80 pears

Q22) A farmer has some ducks and chickens. 3/8   of the number of ducks is equal to 1/4   of the number of chickens.

(a) If the farmer has 420 more chickens, how many ducks does he have?
(b) If the farmer sold 1/2   of his chickens and 2/3   of his ducks, find the ratio of the number of chickens left to the number of ducks left.
 
Give your answer in the simplest form.


Ans:
(a)_______________________
 
(b)_______________________
Answer
a) 840 ducks
b) 9 : 4

Q23) The ratio of the number of guppies to the number of angel fish in Ben's fish tank was 5 : 3 at first. When 55 more guppies were added to the tank, the new ratio of the number guppies to that of the angel fish became 15 : 6.
(a) What was the original number of guppies in the tank?
(b) The next day, Ben wanted the new ratio of the number of guppies to that of the angel fish to be 7 : 3, how many guppies should he take out of the tank?
Ans:(a)__________________
        (b)__________________ 
Answer
a) 110 guppies
 b) 11 guppies

Q24) Yoyo bought a blouse for $36 and a dress that cost $15. What was the ratio of the cost of the dress to the cost of the blouse? Give your answer in the simplest form.



Ans: _______________
Answer
5 : 12

Q25) If Devi has 4 times as many apples as Eileen and Eileen has twice as many apples as Farid, what is the ratio of the number of Devi's apples to the number of Eileen's apples to the number of Farid's apples?



Ans: _______________
Answer
8 : 2 : 1

Q26) In a certain school, 632 pupils sat for the PSLE. The ratio of the number of passes to the number of failures was 7:1. How many pupils passed the PSLE?

Ans:_________________

Answer

553

Q27) The average savings of Amy, Brad, Choon Ming and Devi is $75. The ratio of the total savings of Amy and Brad to the total savings of Choon Ming and Devi is 7 : 3. Choon Ming's savings is 1/4${\displaystyle \frac{1}{4}\mathrm{ }}$  that of Devi's. Find the average savings of Amy, Brad and Choon Ming.

Ans:_________________________

$76

Q28)  The total mass of boxes A, B and C is 28 kg. The ratio of the mass of box A to that of box B to that of box C is 1:2:4. Find the mass of box C.

Ans: _________________ kg

Answer

16

Q29)  Lucy and Siti shared 60 stickers in the ratio of 1 : 3. After Lucy had given some stickers to Siti, the ratio became 1 : 5. How many stickers did Lucy give Siti?

Ans:_________________________

Answer

5 stickers

Q30) Ahmad and Nora share some paper clips in the ratio 9 : 5. After Ahmad has given Nora 24 paper clips, the have the same number of paper clips. How many paper clips do they have altogether?



Ans: ______________
 Answer
168

Q31) Lenny has a total of 156 red and blue pens in the ratio 7 : 6. After giving away an equal number of each type of pen, the number of red and blue pens left was in the ratio 7 : 3. How many pens did she give away altogether?



Ans: _______________
Answer
She gave away 126 pens altogether

Q32) The diagram shows four ribbons A, B, C and D.


Given that the total length of A, B, C and D is 235 cm, find the ratio of the length of A : C.


Ans: _______________
Answer
5 : 6

Q33) A class was fixing a puzzle of their photos. In the first hour, the ratio of the number of fixed pieces to unfixed pieces is 1 : 5. In the next hour, they fixed another 15 pieces of the puzzle. Finally, the number of fixed pieces became 60% of the unfixed pieces. How many pieces were there in the puzzle?



Ans: ________________
Answer
72

Q34) The number of $88, $128 and $198 tickets for a concert are in the ratio 9 : 4 : 3. All the tickets for the concert were sold out. The amount collected from the $128 tickets is $704 000. What is the total amount of money collected from the concert?




Ans: _________________
Answer
$2 609 750

Q35) The ratio of the number of marbles Mike has to the number of marbles Priscilla has is 1 : 3. The ratio of the number of marbles Priscilla has to the number of marbles Lydia has is 6 : 7. If Mike has 15 marbles less than Lydia, how many marbles does Priscilla have?




Ans: ________________ marbles
Answer
18

Q36) In a school, the ratio of the number of pupils who wear glasses to the number of pupils who do not wear glasses is 11 : 5. 2/3​  of the boys and 7/10​  of the girls wear glasses. What is the ratio of the number of boys to the number of girls?




Ans: _______________
Answer
The ratio is 3 : 5

Q37)  The number of marbles in Box A, Box B and Box C was 195.
John added 60 marbles to those in Box A, doubled the number of marbles in Box B and halved the number of marbles in Box C.
The ratio of the number of marbles becomes 4 : 1 : 2.
What is the total number of marbles in the three boxes now?


Answer:_______________________________
Answer
210

Q38) There were 72 pupils in the school hall at first. Then another 15 boys and 21 girls walked into the school hall. The ratio of the number of boys to the number of girls became 4 : 5. How many boys were there in the school hall at first?


Answer: _________________________
Answer
33

Q39) Mr Seng spent $60 on some apples, mangoes and pears in the ratio 3 : 5 : 2. The number of apples was twice the number of mangoes.The number of pears was 13​ the number of apples. The mangoes were sold at 3 for $5. How many fruits did he buy altogether?


Answer:_________________________________
Answer
66

Q40) The ratio of the number of flats to the number of condominiums in a town was 3 : 8. After more condominiums were launched, 20% of the total number of housing was flats. What was the percentage increase in the number of condominiums?



Ans: _______________%
Answer
50

Q41) There are only Chinese and Malay children in a concert hall. The ratio of the number of girls to the number of boys is 3 : 2. The ratio of the number of Chinese boys to the number of Malay boys is 5 : 2. There are 126 more Chinese boys than Malay boys. How many girls are there in the concert hall?


Ans: _______________________
Answer
441 girls

Q42) The ratio of the length to the breadth of a rectangle is 7 : 5. The length of the rectangle is 28 cm. Find the ratio of the breadth to the perimeter of the rectangle.



Ans: _______________

Answer

5 : 24

Q43) Ben swam 15 laps in the morning and 10 more laps in the evening than in the morning. Express the ratio of the number of laps Ben swam in the evening to the total number of laps he swam that day.


Ans: ________________

Answer

5 : 8

Q44) The ratio of the number of teachers to the number of pupils in a school is 1 : 20, If there are 570 more pupils than teachers, how many teachers are there in the school?

Ans: ________________
Answer
30 teachers

Q45) In a soccer stadium, the number of female to the male spectators is 3 : 7. After 287 female and 287 males left the stadium, the ratio of female to male spectators became 2 : 5.
How many spectators were there at first?

Ans: ________________
Answer
8610

Q46) The ratio of the number of boys to the number of girls in a class is 2 : 3. After 4 girls left the class, there are 45​  as many boys as girls. How many pupils are there in the class at first?

Ans: _____________________
Answer
40 pupils

Q47) The figure below, not drawn to scale, shows 2 overlapping similar rectangles. 4/9​ of each rectangle is shaded. Express the shaded area as a ratio of the whole figure.




Answer: _________________________

Answer

2 : 7

Q48) 300 pupils took part in the NAPHA test in April. The table below shows the results of the Spell Bee test.

What is the ratio of the number of pupils who were awarded the badges to the number of pupils who were not awarded the badges?

 Answer: _____________________

Answer

4 : 1

Q49) A basket contained some peaches and apricot. The ratio of the number of peaches to the number of apricots was 1 : 2. When 104 more peaches were put into the basket, the ratio of the number of peaches to the number of apricots became 11 : 6. How many fruits were there in the basket at first?

Ans: _____________
 Answer
There were 117 fruits in the basket at first.

Q50) In a school library, there are 3 Chinese Language books for every 5 English Language books. The number of Malay Language book is 5/9​  as many as the Chinese Language books. Find the ratio of the number of Malay Language books to the number of English Language books.
(Express your answer in its simplest form.)

Ans: ________________
Answer
1 : 3

Q51) Find the missing number.

18 : 4 : 6 = ______ : 10 : 15

Ans : ______________
Answer
45

Q52) Josephine had a total of 540 Singapore and Malaysian stamps in the ratio 11 : 7. After she had given away an equal number of each type of stamps, the number of Singapore and Malaysian stamps left was in the ratio 7 : 1. How many Singapore stamps did she give away?
 
Ans: _____________
 Answer
She gave away 190 stamps.

Q53) Farja and Chelvan caught some worms for a fishing trip. The number of worms that Farja found was 59​  of what Chelvan found. Find the ratio of the number of worms that Farja found to the total number of worms that they found altogether.

Ans: _____________
Answer
5 : 14

Q54) The ratio of the number of motorcycles to the number of lorries in a car park is 5 : 7. If 24 motorcycles left the car park and 24 lorries entered the car park, there would be thrice as many lorries as motorcycles. How many motorcycles are there in the car park?

Ans: _______________
Answer
There are 60 motorcycles in the car park.

Q55) The ratio of the number of boys to that of girls in a drama school is 5 : 3. There are 64 Indian pupils and the rest are Chinese. The ratio of the number of Chinese pupils to the number of Indian pupils is 2 : 1. If there are 32 Indian boys, what is the ratio of the number of Chinese boys to that of Chinese girls?

Ans: _______________
Answer
The ratio of Chinese boys to that of Chinese girls is 11 : 5.

Q56) The ratio of the number of apples to the number of oranges to the number of pears is 8 : 6 : 3. If there are 138 more oranges than pears, how many apples are there altogether?

Ans: ____________
Answer
368

Q57) Alex, Eugene and Terence shared a total of 102 stamps in the ratio of 4 : 7 : 6. After Eugene and Terence gave a total of 10 stamps to Alex, the three boys had an equal number of stamps. How many stamps did Eugene give to Alex?
 
Ans: ___________________
Answer
8 

Q58) The ratio of the number of shirts to the number of dresses is 2 : 7. The ratio of the number of shirts to the number of pants is 3 : 4. What is the ratio of the number of shirts to the number of dresses to the number of pants?

Answer

The ratio of the number of shirts to the number of dresses to the number of pants is 6 : 21 : 8.

Q59) The total amount of water in a tank and a pail is 630 l . If 52.7 l  of water are tranferred from the pail to the tank, the amount of water in the tank will be eight times the amount of water in the pail. How many more millilitres of water were there in the tank than the pail at first?

Ans: ______________ ml 

Answer

There is 384 600 ml  more water in the tank than in the pail at first.

Q60) The total amount of water in bottles A, B and C was 290 ml . After Jamie poured away half of the water from bottle A, doubled the amount of water in bottle B and added 30 ml  of water into bottle C, the ratio of the amount of water in bottle A to B to C was 3 : 2 : 1. Find the total amount of water in the 3 bottles in the end.

Ans: ____________ml 

Answer

The total amount of water in the 3 bottles at the end is 240 ml . 

Q61) Susan and Jane shared some stickers in the ratio of 5 : 7. After they gave away 117 stickers each, the ratio of Susan's stickers to Jane's stickers was then 1 : 4.

(a) Find the number of stickers that Jane had at first.

(b) If Susan gave away another 12 stickers, how many stickers would she

     have left?

Ans: (a) _____________

        (b) _____________

 Answer

(a) Jane had 189 stickers at first.

(b) Susan would have 6 stickers left.

Q62) Sharifah and Ainah collected some pink and green ribbons. Sharifah had a total of 192 ribbons. The ratio of the number of pink ribbons to the number of green ribbons Sharifah had collected was 3 : 5. The ration of the number of pink ribbons to the number of green ribbons Ainah had collected was 1 : 2. If Sharifah had collected 4 times as many ribbons as Ainah, find the ratio of the number of pink ribbons Sharifah had to the number of green ribbons Ainah had.

Ans: ______________________

Answer

9 : 14

Q63) Company A and Company B hired the same number of workers.
The ratio of number of female workers to the number of male workers hired by Company A and Company B was 1:3 and 1:4 respectively.

(a) Company B had hired 20 more male workers than Company A. How many workers did Company A hire?
(b) Half a year later, equal number of female workers left Company A and B. The ratio of the number of female workers to the number of male workers hired by Company A and Company B became 2:3 and 2:5 respectively. How many female workers left both companies?


Ans:
(a) ___________
(b) ___________

Answer

(a) 400 workers
(b) 60 female workers

Q64) The ratio of the number of pears to the number of mangoes in Basket A and in Basket B are 2:1 and 2:7 respectively. Basket A has 23​  times as many fruits as Basket B.
(a) Find the ratio of the number of pears in Basket B to the number of pears in Basket A.
(b) When 18 mangoes are moved from Basket B to Basket A, the ratio of the number of pears to the number of mangoes in Basket A becomes 8:7. How many mangoes are there in Basket A now?


Ans:
(a) __________
(b) __________

​ Answer
(a) 1:2
(b) 42 mangoes

Q65) Michael, Jeremy and Andrew shared 320 marbles in the ratio 1 : 2 : 5. Jeremy lost 12​  of his marbles to Michael in the first round of game and Andrew lost 12​  of his marbles to Jeremy in the second round of game.

a) Find the ratio of the number of Michael's marbles to Jeremy marbles to Andrew's marbles after two round of games.

b) How many more marbles will Jeremy have than Michael if Andrew gave Michael 10 marbles after the second game?

Ans:

a)______________

b)______________

Answer

a) 4 : 7 : 5

b) 50 marbles

Q66) There was a car exhibition at the Singapore Expo. 29​  of the visitors were children. There were 4 000 more adults than children. The ratio of the number of boys to the number of girls was 3 : 5. The ratio of the number of men to the number of women was 3 : 1. Find the number of all male visitors in the car exhibition.

Ans:______________

Answer

4 800 male visitors

Q67) Marcus, Larry and Joe shared some stickers. On average, each boy had 42 stickers. After each boy bought another 20 stickers, the ratio of Marcus's stickers to Larry's to Joe's is 2 : 1 : 3. How many stickers did Larry have now?

Ans:______________ 

Answer

31 stickers

Q68) Peter, James and Reuben had some cards. Peter and Reuben had 325 cards altogether. James and Reuben together had 3 times as many cards as Peter. The ratio of the number of cards James had to the number of cards Reuben had was 3 : 9.

How many cards did Peter have?

Ans:_______________ 

Answer

100 cards

Q69) 46% of the books in a bookshop are English books. The rest are Chinese and Malay books. The ratio of the number of Chinese books to the number of Malay books is 2 : 7. There are 90 more English books than Malay books.

(a) What percentage of the books are Malay books?

(b) How many books are there altogether?

Ans: (a)______________ 
         (b)______________ 

 
Answer

a) 42%

b) 2250 books

Q70) The ratio of the number of guppies to the number of angel fish in Ben's fish tank was 5 : 3 at first. When 55 more guppies were added to the tank, the new ratio of the number guppies to that of the angel fish became 15 : 6.

(a) What was the original number of guppies in the tank?

(b) The next day, Ben wanted the new ratio of the number of guppies to that of the angel fish to be 7 : 3, how many guppies should he take out of the tank?

Ans:(a)__________________ 

        (b)__________________ 

Answer

a) 110 guppies

b) 11 guppies

Q71) The number of red watches to the number of blue watches to the number of yellow watches are in the ratio 2 : 5 : 8. After Mr Lee sold 14  of the yellow watches, he had 56 more yellow watches than red watches. Find the total number of watches at first.
Answer:________________________
Answer
210

Q72) There are two tins of biscuits, Y and Z. The ratio of the mass of Y to the mass of Z is 4 : 1. If 26 g of biscuits is transferred from Y to Z, the ratio of the mass of Y to the mass of Z is 7 : 5. Find the total mass of the 2 tins of biscuits.
 
Answer: _________________
Answer
120 g 

Q73) Sally had apples and mangoes in the ratiop 8 : 5. She sold 117 apples and the ratio of the number of appples to the number of mangoes became 5 : 8.
a) Find the number of mangoes Sally had.
 b) How many apples had Sally at the beginning?
 
a) Ans:__________________
 
b) Ans:__________________
Answer
a) 120 mangoes
 b) 192 apples

Q74) The ratio of the number of boys to the number of girls to the number of teachers in Ace Primary School is 39 : 26 : 2. If there are 52 teachers in the school,
(a) find the number of boys in the school,
(b) find the total number of pupils and teachers in the school.
Answer:
​​​​​​​(a) ______________ 
(b) ______________ 
Answer
(a) 1014
 (b) 1724

Q75) Container A and Container B are identical. Container A is 1/2   filled with sand while Container B is 1/5   filled with sand. The ratio of the total mass of Container A and its contents to the total mass of Container B and its contents is 7 : 5. The total mass of the two containers with their contents is 1440g.
What is the mass of each empty container?
Answer: ________________ 
Answer
440 g

Q76) Last year, a fitness club had a total of 96 members. The ratio of the number of male members to the number of female members was 5 : 3. When 54 new members joined the club this year, the ratio of male to female members became 3 : 2.
a) How many of the new members who joined this year are female?
b) What is the ratio of the number of female members last year to the number of female members this year?
Answer
a) 2,4 of the new members are female.
b) The ratio is 3 : 5.

Q77) At Baba Shopping center, 18  of the patrons are children. The ratio of the number of men to the number of women is 5 : 9. The ratio of the number of boys to the number of girls is 2 : 3.
a) What is the ratio of the number of children to the number of men to the number of women?
b) There are 360 more women than men. How many boys were there at the shopping center?
 
Answer:(a)____________________
              (b)____________________
Answer
a) 1 : 5 : 9
b) 72 boys

Q78) Mrie bought a large bouquet of flowers. 2/5   of the flowers were daisies and the rest were orange and purple tulips in the ratio 4 : 5.
a) What fraction of the flowers were orange tulips?
b) There were 8 more purple tulips than orange tulips. How many flowers were there in the bouquet?
 
Answer : (a) _______________ 
                (b) _______________ 
 Answer
a) 4/15  
 b) 120 flowers

Q79) A fruit stall had 720 fruits for sale. 1/4  of them were apples, 20% of the remaining fruits were pears and the rest were oranges. 48 apples, 24 pears and 12 oranges were sold.
(a) How many oranges were there at the beginning?
(b) Find the ratio of the total number of fruits sold to the total number of fruits in the beginning. Express your answer in the simplest form.
Ans:(a)_______________ 
        (b)_______________ 
Answer
a) 432 oranges
b) 7 : 60