Question 1

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 2

A sum of Rs.312 was divided among 100 boys and girls in such a way that the boy gets Rs.3.60 and each girl Rs. 2.40 the number of girls is

Accepted Answer

40

Question 3

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 4

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 5

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

Accepted Answer

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

Question 6

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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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 15

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 16

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

Question 17

Divide Rs.6500 among A, B and C so that after spending 90%, 75% and 60% of their respective saving was in the ratio of 3: 5: 6

Accepted Answer

A's spending 90% therefore saving = 10% B's spending 75% therefore saving = 25% C's spending 60% therefore saving = 40% Let us suppose A, B and C saves Rs. 3, 5 and 6 respectively. 10% of A's saving = Rs. 3 100% of A's saving = (3/10)*100 = Rs. 30 25% of B's saving = Rs. 5 100% of B's saving = (5/25)*100 = Rs. 20 40% of C's saving = Rs.6 100% of C's saving = (6/40)*100 = Rs. 15 Divide Rs. 6500 in the ratio of 30 : 20 : 15 A's Share = (30/65)*6500 = Rs. 3000 B's Share = (20/65)*6500 = Rs. 2000 C's Share = (15/65)*6500 = Rs. 1500

Question 18

The ratio of male and female in a city is 7 : 8 respectively and percentage of children among male and female is 25 and 20 respectively. If number of adult females is 156800, what is the total population of the city?

Accepted Answer

Let the total population be 'p' Given ratio of male and female in a city is 7 : 8 In that percentage of children among male and female is 25% and 20% => Adults male and female % = 75% & 80% But given adult females is = 156800 => 80%(8p/15) = 156800 => 80 x 8p/15 x 100 = 156800 => p = 156800 x 15 x 100/80 x 8 => p = 367500 Therefore, the total population of the city = p = 367500

Question 19

The third proportional to x2-y2 and x-y is :

Accepted Answer

Let the third proportional to x 2 - y 2 and x - y be z. Then, x 2 - y 2 : x - y : : x - y : z = > x 2 - y 2 * z = x - y 2 => z= x - y 2 x 2 - y 2 = x - y x + y

Question 20

If 76 is divided into four parts proportional to 7, 5, 3, 4, then the smallest part is:

Accepted Answer

Given ratio = 7 : 5 : 3 : 4, Sum of ratio terms = 19. Smallest part = (76*3/19) = 12

Ratio and Proportion Questions