 # Ratio and Proportion Aptitude Questions with Solutions with PDF at Smartkeeda | Ratio & Proportion Quiz 5 at Smartkeeda

Important for :
1
In the income statement of Asha and Ravenna, the ratio of their income in the year 2017 was 5 : 4. The ratio of Asha’s income in the year 2018 to that in 2017 is 3 : 5 and the ratio of Ravenna’s income in the year 2018 to that in 2017 is 3 : 2. If Rs. 10242 is the sum of the income of Asha and Ravenna in the year 2018, then find the income of Ravenna in the year 2017?
» Explain it
E
Let the income of Asha in 2018 and 2017 be 3x and 5x respectively.

Let the income of Ravenna in 2018 and 2017 be 3y and 2y respectively

Since, the ratio of their income in the year 2017 was 5 : 4

5x : 2y = 5 : 4

2x = y

The sum of their incomes in 2018 is Rs. 10242

3x + 3y = 10, 242

9x = 10, 242

x = 1,138 and y = 2276

Ravenna’s income for the year 2017 = 2y = Rs. 4552

Hence, option E is correct.
2
Two vessels A and B of equal volume contain milk and water in the ratio 3 : 2 and 2 : 1 to their brim respectively. Two litres of the solution from vessel A and three litres of the solution from vessel B are poured into a big empty vessel C. If the solution in C occupied 40% of the capacity of C, what proportion of the volume of vessel C should be the volume of water that shall be added so that the ratio of milk and water in vessel C becomes 1 : 1?
» Explain it
D
Amount of milk poured into C from vessel A and B

 = 2 × 3 + 3 × 2 = 16 litres 5 3 5

Also, amount of water poured into C from vessels A and B
 = 5 – 16 = 9 litres 5 5

Given, 5 litres represent 40% of the capacity of vessel C, vessel C has a capacity of
 = 5 × 5 = 12.5 litres 2

To make the quantities of water and milk same in the vessel C, quantity of water to be added
 = 16 – 9 = 7 litres 5 5 5

 Therefore, reqd. answer = 7/5 = 14 12.5 125

Hence, option D is correct.
3
The average score in an examination taken by 52 students of a class is 85. If the scores of the best 5 performers are not considered, the average score of the remaining students falls by 2. If, none of the first five highest scorers is not below 80 and if each of the 5 top scorers had distinct integral scores, find the maximum possible score of the topper.
» Explain it
D
Let the score of the topper be T.

Total score of the 52 students = 52 × 85 = 4420

Total score of the remaining 47 students after scores of the best five performers are removed = 47 × 83 = 3901

Total score of the top five students = 4420 – 3901 = 519

T + (total score of the next 4 top scores) = 519

T is the maximum when the total score of the next 4 top scorers is minimum.

Total score of the next 4 top scorers has a minimum value of 80 + 81 + 82 + 83 = 326 (since all the top 5 scores are distinct) and the least is 80.

T has a maximum value of 519 – 326 = 193

Hence, option D is correct.
4
A bag contains certain number of coins of different denominations. The ratio of the number of Rs. 1 coins to Rs. 2 coins is 5 : 7, respectively and the ratio of number of Rs. 2 coins to Rs. 5 coins is 7 : 6 respectively. Find the total value of the Rs. 5 coins, if the total value of the Rs. 1 coins in the bag is Rs. 15.
» Explain it
B
Ratio of the number of coins of denominations Rs. 1 : Rs. 2 : Rs. 5 = 5 : 7 : 6

Let, the number of coins of Rs. 1, Rs. 2 and Rs. 5 in the bag be 5x, 7x and 6x.

Since, the total value of Rs. 1 coin in the bag is Rs. 15

So, the number of coins of Rs. 1 in a bag = 15

5x = 15 , ⇒ x = 3

Therefore, number of Rs. 5 coins in the bag = 6x = 18

So, required value of Rs. 5 coins = 6 × 3 × 5 = Rs.90

Hence, option B is correct.
5
A father distributed some chocolates among his four children and kept some with him. The eldest three children got chocolates in the ratio 3 : 11 : 7. The total number of chocolates with father and youngest child is three times the total chocolates with the three eldest children. The ratio of chocolates with father and that with all the children is 3 : 4. Find the total number of chocolates if the youngest child has 81 chocolates with him?
» Explain it
B
Let the children be P, Q, R and S and Father be F

Chocolates with P : Q : R= 3 : 7 : 11

Let the number of chocolates be 3k, 7k and 11k

Total chocolates with three eldest children = 21k

Chocolate with F and S = 3 × 21k = 63k

Total chocolates = (21k + 63k) = 84k

Chocolate with F : (P + Q + R + S) = 3 : 4

Total 7 units of chocolate = 84 k

1 unit = 12k

Chocolate with F = 3 × 12k = 36k

Chocolate with S =  (63k – 36k) = 27k

27 k = 81  →  k=3

Total number of chocolates = 84k = 84 × 3 = 252

Hence, option B is correct.
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