Ratio and Proportion with Explanation

Q8. 20 litres of the mixture has water and milk in the ratio 3 : 5. If 4 litres of the mixture is to be replaced by 4 litres of milk, then what is the ratio of water to milk in the new mixture?

Answer- Option B

Explanation-

Quantity of milk in 16 litres of mixture =

16

x

5 8

litres = 10 litres

Quantity of milk in 20 litres of new mixture = (10 + 4) litres
Quantity of water in it = (20 - 14) litres = 6 litres
Ratio of water and milk in the new mixture is 6 : 14 = 3 : 7

Q9. In a school, there are 200 girls and the ratio of the number of girls to boys is 4 : 9. Then how many students are there in the school?

Answer- Option C

Explanation-

Let the number of girls and boys be 4x and 9x respectively
Then, 4x = 200
x = 50
Total number of students in the school = 13x = 650

Q10. An amount of Rs. 366 is to be divided among P, Q, and R in such a manner that Q gets two-third as much as P and R together, and P may get half as much as Q and R together. What is the share of P?

Answer- Option B

Explanation-

According to the question,
Q =

2 3

(P + R), P =

1 2

(Q + R)

On solving these two equation, we obtain R =

4 5

P and Q =

6 5

P

Now, P + Q + R = Rs. 366
P +

6 5

P +

4 5

P = 366

P = Rs. 122

Q11. Seats for Computer Science, Mechanical, and Electronics in a university are in the ratio 7 : 5 : 8. There is a planning to increase these seats by 50%, 40%, and 75% respectively. Find the ratio of increased seats?

Answer- Option D

Explanation-

Let the seats for Computer Science, Mechanical, and Electronics be 7x, 5x and 8x respectively
After incrementation,
Seats for Computer Science = 150% of 7x =

21x 2

Seats for Mechanical = 140% of 5x = 7x
Seats for Electronics = 175% of 8x = 14x
New ratio will be

21x 2

: 7x : 14x = 3 : 2 : 4

Q12. An alloy contains iron and nickel in the ratio 8 : 3. Find the quantity of iron required to be melted with 21 kg of nickel?

Answer- Option C

Explanation-

Let iron and nickel in an alloy be 8x and 3x respectively
Then, 3x = 21
x = 7
Quantity of iron = 8x = 56 kg

Q13. Divide Rs. 1328 among three boys Suresh, Ramesh, and Ganesh in the ratio 34 : 26 : 23. The sum of Suresh and Ganesh share is

Answer- Option A

Explanation-

Sum of ratio = 34 + 26 + 23 = 83
Suresh's share = Rs.

34 83

x

1328

= Rs. 544

Ganesh's share = Rs.

23 83

x

1328

= Rs. 368

(Suresh + Ganesh)'s share = Rs. (544 + 368) = Rs. 912

Q14. A Father has 735 toffees and wants to distribute among his 3 children A, B, and C. If each child had received 25 less toffees, their shares would have been in the ratio 1 : 3 : 2. The number of toffees received by C is

Answer- Option B

Explanation-

Total number of toffees received by children = (735 - 25x3) = 660
Number of toffees received by C is

660

x

2 6

+ 25

= 225