Question 1

There is certain numbers of toys in the box. They are divided into such a way that the person who gets 1/4 of the whole gets thrice of what the others get on an average. Find the number of people amongst whom the toys are distributed?

Accepted Answer

If the person who gets 1/4 of the whole gets thrice of what the others get on an average, each one will get =1/3×1/4=112 of the whole. Therefore, if there are k persons other than the person who gets one-fourth, then 1/4 + k/12 = 1 ⇒ k=9 Hence, total number of people = 10.

Question 2

16 : 56 :: 32 : ?

Accepted Answer

16 : 56 :: 32 : ? Let the required number be 'n' The given numbers follow a logic that, 16/56 = 2/7 => 32/n = 2/7 => 32 x 7/2 = n => n = 112. Hence, 16 : 56 :: 32 : 112.

Question 3

Pencils, Pens and Exercise books in a shop are in the ratio of 10: 2 : 3. If there are 120 pencils, the number of exercise books in the shop is:

Accepted Answer

Let Pencils = 10x, Pens = 2x & Exercise books = 3x. Now, 10x = 120 hence x = 12. Number of exercise books = 3x = 36.

Question 4

In a cricket match total number of runs scored by Virat, Dhoni and Rohit is 285. The ratio of the number of runs scored by Virat and Rohit is 3 : 2 and that of the runs scored by Rohit and Dhoni is also 3 : 2. The number of runs scored by Virat in t…

Accepted Answer

From the given data, Virat : Rohit = 3 : 2 Rohit : Dhoni = 3 : 2 Ratio of runs scored by Virat, Rohit and Dhoni respectively = 3 x 3 : 2 x 3 : 2 x 2 9 : 6 : 4 Runs scored by Virat = 9/19 x 285 = 135.

Question 5

In a class of 39 students the ratio of boys and girls is 2 : 1. Radhika ranks 15th among all the students from top and 8th among girls from bottom. How many boys are there below Radhika ?

Accepted Answer

Total student= 39, boys : girls = 2:1, hence no of boys= 2/3(39)= 26 num of girls= 1/3(39) = 13 , since radhika ranked 15 among 39 student from top and ranked 8 among girls from bottom , this means 7 girls are below radhika, rest 13-9= 5 girls are above her, now from 14 toper 5 are girls hence 14-5=9 boys. Hence num of boys below radhika are 26-9=17

Question 6

If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days?

Accepted Answer

12 m e n 120 a c r e s 36 d a y s 54 m e n ? 54 d a y s As 12 men can reap 120 acres, 54 men will be able to reap more acres in 36 days, 120 acres of land was reaped, so in 54 days, more land will be reaped. Thus, the numbers of acres that can be reaped by 54 men in 54 days = 54 12 x 120 x 54 36 = 810 acres

Question 7

Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct?

Accepted Answer

At the moment the paint is 3 liters of paint and 3 liters of water. We need to add to this to make the new ratio 2 liters paint to 1.5 liters water. As this is equivalent to 4 : 3 we can see that we have the right amount of water, and just need 1 liter of paint to make it correct.

Question 8

Rs. 2600 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4 ?

Accepted Answer

1/2:1/3:1/4 = 6:4:3 As the difference is 3 => 3/13x2600 = 600

Question 9

Two vessel P and Q contain milk and water in ratio 3 : 2 and 5 : 3 respectively. If 10 liters of the mixture is removed from vessels P and poured in vessel Q then ratio of milk to water in vessel Q becomes 8 : 5. Find the initial quantity of water i…

Accepted Answer

Given ratio of initial mixture of milk and water in Q = 5 : 3 Let the initial quantity of mixture in vessel Q = 8x Let quantity of Milk = 5x and Let quantity of water = 3x According to the question, 5 x + 10 x 3 5 3 x + 10 x 2 5 = 8 5 => 25x + 30 = 24x + 32 => x = 2 Required Initial quantity of milk = 5x = 5 x 2 = 10 lit.

Question 10

Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats ?

Accepted Answer

Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. Seats for Mathematics, Physics and Biology in a school are 5x, 7x and 8x. There is a proposal to increase these seats by 40%, 50% and 75% respectively. Then Seats for Mathematics, Physics and Biology in a school will be 1.4 X 5x, 1.5 X 7x and 1.75 X 8x and ratio will be 7 : 10.5 : 14 => 2:3:4.

Question 11

Maneela, Raghu and Aravind have some jems with each of them. Five times the number of jems with Raghu equals seven times the number of jems with Maneela while five times the number of jems with Maneela equals seven times the number of jems with Arav…

Accepted Answer

From given data, R : M = 5 : 7 M : A = 5 : 7 R : M : A = 25 : 35 : 49 25 + 35 + 49 = 109

Question 12

There are two containers, the first one contains 1 litre pure water and the second one contains 1 litre pure milk.Now 5 cups of water from the first container is taken out is mixed well in the second container. Then, 5 cups of this mixture is taken …

Accepted Answer

Here the ratio of mixtures( i.e milk , water) doesnot matter. But the important point is that whether the total amount ( either pure or mixture ) being transferred is equal or not.Since the total amount ( i.e 5 cups) being transferred from each one to another , hence A =B.

Question 13

Two solutions have milk & water in the ratio 7:5 and 6:11. Find the proportion in which these two solutions should Be mixed so that the resulting solution has 1 part milk and 2 parts water ?

Accepted Answer

To get the solution that contains 1 part of milk and two parts of water, they must be mixed in the ratio as 7x+6x/5y+11y = 1/2 26x = 16y x/y = 16/26 x/y = 8/13

Question 14

64 boys and 40 girls form a group for social work. During their membership drive, the same number of boys and girls joined the group. How many members does the group have now, if the ratio of boys to girls is 4:3 ?

Accepted Answer

Let us say x boys and x girls joined the group. (64 + x)/(40 + x) = 4/3 192 + 3x = 160 + 4x => x = 32 Number of members in the group = 64 + x + 40 + x = 104 + 2x = 168.

Question 15

The ratio of students in a coaching preparing for B.tech and MBA is 4 : 5. The ratio of fees collected from each of B.tech and MBA students is 25 : 16. If the total amount collected from all the students is 1.62 lakh, what is the total amount collec…

Accepted Answer

The ratio of fees collected from B.Tech : MBA = 4x * 25y : 5x * 16y = 100xy : 80xy = 5xy : 4 xy = 5k : 4k The amount collected only from MBA students = 4 9 × 1 . 62 l a k h = Rs. 72,000

Question 16

A man spend Rs. 810 in buying trouser at Rs. 70 each and shirt at Rs. 30 each. What will be the ratio of trouser and shirt when the maximum number of trouser is purchased ?

Accepted Answer

Let us assume S as number of shirts and T as number of trousers Given that each trouser cost = Rs.70 and that of shirt = Rs.30 Therefore, 70 T + 30 S = 810 => 7T + 3S = 81......(1) T = ( 81 - 3S )/7 We need to find the least value of S which will make (81 - 3S) divisible by 7 to get maximum value of T Simplifying by taking 3 as common factor i.e, 3(27-S) / 7 In the above equation least value of S as 6 so that 27- 3S becomes divisible by 7 Hence T = (81-3xS)/7 = (81-3x6)/7 = 63/7 = 9 Hence for S, put T in eq(1), we get S = 81-7(9)/3 = 81-63 / 3 = 18/3 = 6. The ratio of T:S = 9:6 = 3:2.

Question 17

A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year ?

Accepted Answer

A : B (8000x4)+(4000x8) : (9000x6)+(6000x6) 64000 : 90000 => 32 : 45

Question 18

In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per …

Accepted Answer

Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier) = (1200)(30)(3) kg. Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k As the same provisions are available => (1200)(30)(3) = (1200 + x)(25)(2.5) x = ([(1200)(30)(3)] / (25)(2.5)) - 1200 => x = 528.

Ratio and Proportion Questions