Can you solve these ratio and proportion questions?

This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests. Sumit hired a travelling car for a tour. If the car is rented for 8 hours or less, […]

This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests.

Sumit hired a travelling car for a tour. If the car is rented for 8 hours or less, the charge is Rs 100 per hour or Rs 8 per km whichever is more. On the other hand, if the car is rented for more than 8 hours, the charge is Rs 80 per hour or Rs 6 per km, whichever is more. Sumit used the car for 120 km and paid Rs 800. For how many hours did he take the car for rent?

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a) 5 hours b) 6 hours c) 9 hours d) 10 hours

Ans: d

Solution: Let the car be rented for 8 hours or less Then the number of hours it is rented for = 800/100 = 8 hours
But if it charged Rs 8 per km, the amount that should paid be 120(8) = 960 But he paid only Rs 800 Number of hours = 800/100 = 10 hours
If it is charged at Rs 6 per km, the amount that should paid be 120(6) = Rs 720 which is less than Rs 800 Sumit rented car for 10 hours.

The ratio of marks obtained by Shubham in theory to the total marks which can be obtained in theory is 7 : 10. Total marks which can be obtained in practicals were 20% of the total marks of theory. If Shubham got full marks in practical, then find the ratio of total marks obtained by Shubham to the total marks which can be obtained in the subject (theory + practical).

a) 2 : 3 b) 1 : 2 c) 3 : 4 d) 5 : 6

Ans: c

Solution: Let, marks obtained by Shubham in theory and total marks of theory be ‘7x’ and ‘10x’ respectively
So, total marks (theory + practical) = 10x + 2x = 12x Marks obtained by shubham (theory + practical) = 7x + 2x = 9x
So, required ratio = 9x/12x = 3/4 = 3:4

Incomes of John and Kelvin are in the ratio 4:7 and their spending are in the ratio 6:11. If John saves one third of his income, then what will be the ratio of their savings.

a) 12 : 19 b) 12 : 13 c) 14 : 15 d) 18 : 19

Ans : a

Solution: Let the income of
John 4x,
Kelvin 7x
And expenditure be :
John 6y ……….(i)
Kelvin 11y
John spending = John’s earning – John’ s savings
John’s expenditure = 4x – 4x/3 = 8x/3 ……………….(ii)
(i) – (ii)
6/y = 8/3 x ==>; x/y = 9/4
Required ratio = 4x – 6y/ 7x -11y = 4x-(4/9x) 6/ 7x – (4/9x) 11 = 36 – 24/ 63 – 44 = 12/19