Ratio problems made easy

Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment tests.

Hyderabad: 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.

1. The ratio of number of boys to that of girls in a group becomes 2 : 1 when 15 girls leave. But afterwards, when 45 boys also leave, the ratio becomes 1 : 5. Originally the number of girls in the group was?
a) 30 b) 20 c) 10 d) 40
Ans: d
Solution: Let the original number of boys and girls be x and y respectively.
Then x/(y – 15) = 2/1
=>; x = 2y – 30 ……….. (i)

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Again, (x – 45) / (y – 15) = 2/1

=>; 5x – 225 = y – 15

=>; 5x = y – 15 225
=>; 5 (2y–30) = y 210 [From equation (i)]
=>; 10y – 150 = y 210
=>; 10y – y = 210 150
=>; 9y = 360
=>; y = 360/9 = 40
2. The ratio of the number of ladies to that of gents at a party was 3 : 2. When 20 more gents joined the party, the ratio was reversed. The number of ladies present at the party was?

a) 24 b) 30 c) 36 d) 16

Ans: a

Solution: Let the number of ladies and gents be 3x and 2x respectively.

According to the question,

3x / (2x 20) = 2/3

=>; 9x = 4x 40 Þ 5x = 40
=>; x = 8
 Number of ladies = 3x
= 3 × 8 = 24

3. In a school having roll strength 286, the ratio of boys and girls is 8 : 5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes?
a) 4 : 3 b) 4 : 7 c) 5 : 9 d) 2 : 5
Ans: a
Solution: 8 / (8 5) × 286 = 8/13 × 286 = 176
Initially number of boys
 Number of girls
= 5/13 × 286 = 110

22 more girls get admitted.

Required ratio

176 / (110 22) = 176 / 132 = 4/3 = 4 : 3

4. What must be added to each term of the ratio 7 : 11, so as to make it equal to 3 : 4 ?

a) 5 b) 5.5 c) 6.5 d) 7.5

Ans: a

Solution: Let the required number be x.

 (7 x) / (11 x) = 3/4

=>; 28 4x = 33 3x
=>; x = 33 – 28 = 5

5. The number of students in three classes are in the ratio 2 : 3 : 4. If 12 students are increased in each class, this ratio changes to 8 : 11 :14. The total number of students in the three classes at the beginning was?

a) 108 b) 123 c) 154 d) 162

Ans: d

Solution: Let the original number of students be 2x, 3x and 4x in three class.

According to the question,

(2x 12) / (3x 12) = 8/11

=>; 24x 96 = 22x 132
=>; 2x = 132 – 96 = 36
=>; x = 36/2 = 18
Original number of students
= 2x 3x 4x
= 9x = 9 × 18 = 162

To be continued…

M Venkat
Director

MVK Publications

Dilsukhnagar

7671002120