Question 1

A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type respectively.

Accepted Answer

let ratio be x. Hence no. of coins be 5x ,9x , 4x respectively Now given total amount = Rs.206 => (.50)(5x) + (.25)(9x) + (.10)(4x) = 206 we get x = 40 => No. of 50p coins = 200 => No. of 25p coins = 360 => No. of 10p coins = 160

Question 2

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

Accepted Answer

Let the third number be x. Then, first number = 120% of x =120x/100 = 6x/5 Second number =150% of x = 150x/100 = 3x/2 Ratio of first two numbers = 6x/5 : 3x/2 = 12x : 15x = 4 : 5

Question 3

A mixture contains alcohol and water in the ratio 4 : 3. If 5 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.

Accepted Answer

Let the quantity of alcohol and water be 4x litres and 3x litres respectively 4x/(3x+5) = 4/5 20x = 4(3x+5) 8x = 20 x = 2.5 Quantity of alcohol = (4 x 2.5) litres = 10 litres.

Question 4

If Rs. 782 be divided into three parts, proportional to 12:23:34 , then the first part is?

Accepted Answer

R s . 782 * 6 23 Given ratio = 1 2 : 2 3 : 3 4 = 6:8:9 1st part = R s . 782 * 6 23 = Rs. 204

Question 5

Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit's salary?

Accepted Answer

Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively. Then, (2x+4000) / (3x+4000) = 40 / 57 ⇒ 57 × (2x + 4000) = 40 × (3x+4000) ⇒ 6x = 68,000 ⇒ 3x = 34,000 Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000

Question 6

The compounded ratio of (2 : 3), (6: 11) and (11 :2) is

Accepted Answer

Compounded Ratio :: When we compound two or more ratio's with each other through product or multiplication, the result is simply a compound ratio. Thus, the product of two or more ratios; i.e, ab:cd is a ratio compounded of the simple ratios a:c and b:d. Required compounded ratio = (2/3 x 6/11 x 11/2) = 2/1.

Question 7

Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?

Accepted Answer

Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number. US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2. Now US : Indian = 25 : 10, and Indian : British = 10 : 2 Hence the two ratios can be combined and US : British = 25 : 2

Question 8

If 0.75: x :: 5:8, then x is equal to:

Accepted Answer

(x * 5) = (0.75 *8) X=6/5 = 1.20

Question 9

A sum of Rs. 427 is to be divided among A, B and C such that 3 times A’s share, 4 tunes B’s share and 7 times C’s share are all equal. The share of C is :

Accepted Answer

3A = 4B = 7C = k,Then A = k/3, B = k/4 and C= k/7. A : B : C = k/3 : k/4 : k/7 = 28:21 :12. Cs share = Rs. [427 x (12/61)] = Rs. 84

Question 10

In a zoo, there are rabbits and pigeons. If heads are counted, there are 340 heads and if legs are counted there are 1060 legs.How many pigeons are there?

Accepted Answer

Suppose there are all the pigeons then total no of heads are 340 and total no of legs are 680. Now, since 380 (1060-680) legs are extra, it means there will be 190 (380/2) rabbits.As we know a rabbit has two extra legs than that of a pigeon. Therefore, number of rabbits =190 and number of pigeons = 340- 190 = 150

Question 11

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

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively. Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x). ⇒ [(140/100) × 5x],[(150/100) × 7x] and [(175/100) × 8x] ⇒ 7x, 21x/2 and 14x. ⇒ The required ratio =7x : 21x/2 : 14x ⇒ 14x : 21x : 28x ⇒ 2 : 3 : 4

Question 12

The third proportional to 9 and 12 is ?

Accepted Answer

Let the third proportion to 9 & 12 be 'x'. => 9:12 = 12 :p => p = 12x12/9 = 16.

Question 13

The salaries of A, B, and C are in the ratio of 1 : 2 : 3. The salary of B and C together is Rs. 6000. By what percent is the salary of C more than that of A?

Accepted Answer

Let the salaries of A, B, C be x, 2x and 3x respectively. Then,2x + 3x = 6000 => x = 1200. A's salary = Rs. 1200, B's salary = Rs. 2400, and Cs salary Rs. 3600. Excess of C's salary over A's=[ (2400 /1200) x 100] = 200%.

Question 14

A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :

Accepted Answer

Dog : Hare = (3*3) leaps of hare : 5 leaps of hare = 9 : 5.

Question 15

In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is

Accepted Answer

Let the number of boys and girls be 8x and 5x. Total number of students = 13x = 13 * 32 = 416.

Question 16

The concentration of petrol in three different mixtures (petrol and kerosene) is 1/2 , 3/5 and 4/5 respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. what is the ratio of petrol and kerosene in th…

Accepted Answer

Concentration of petrol in A B C 1/2 3/5 4/5 Quantity of petrol taken from A = 1 litre out of 2 litre Quantity of petrol taken from B = 1.8litre out of 3 litre Quantity of petrol taken from C = 0.8 litre out of 1 litre Therefore, total petrol taken out from A, B and C = 1+1.8+0.8 =3.6 litres So, the quantity of kerosen =(2+3+1) - 3.6 =2.4 litre Thus, the ratio of petrol to kerosene = 3.6/2.4 = 3/2

Question 17

Alloy A contains 40% gold and 60% silver. Alloy B contains 35% gold and 40% silver and 25% copper. Alloys A and B are mixed in the ratio of 1:4 .What is the ratio of gold and silver in the newly formed alloy is?

Accepted Answer

Assume the weight of alloy a is 100 kg Therefore, The weight of alloy B is 400kg Gold silver copper A 40kg 60kg 0kg B 140kg 160kg 100kg total 180kg 220kg 100kg Therefore, Ratio of gold and silver in new alloy = 180 500 : 200 500 = 36% :44%

Question 18

The number of oranges in three baskets are in the ratio of 3 : 4 : 5. In which ratio the no. of oranges in first two baskets must be increased so that the new ratio becomes 5 : 4 : 3?

Accepted Answer

Let, B1 : B2 : B3 = 3x : 4x : 5x again B1 : B2 : B3 = 5y : 4y : 3y Since there is increase in no.of oranges in first two baskets only, it means the no. of oranges remains constant in the third basket Therefore, 5x = 3y Hence 3x : 4x : 5x => 9 y 5 : 12 y 5 : 15 y 5 = 9y:12y:15y and 5y : 4y : 3y => 25x : 20x : 15x Therfore, increment in first basket = 16 Increment in second basket = 8 Thus, required ratio = 16/8 = 2:1

Question 19

What is the third proportional to 16 and 36 ?

Accepted Answer

f C is the third proportional to A and B, then A/B = B/C If x is the third proportional to 16 and 36, then 16/36 = 36/x => 4/9 = 36/x => x = 36 * 9/4 => x = 9 * 9 => x = 81

Ratio and Proportion Questions