Question 58

At the beginning of a term, the ratio of the number of boys in a school under 15 years to those over 15 years age was 5: 4. At the end of term,the ratio was 7:8 as of 20 boys had reached the age of 15 years during the term. Find the total number of‘Boys in the school, given that no boy left or was admitted during the term.

Name: At the beginning of a term, the ratio of the number of boys in a school under 15 years to those over 15 years age was 5: 4. At the end of term,the ratio was 7:8 as of 20 boys had reached the age of 15 years during the term. Find the total number of‘Boys in the school, given that no boy left or was admitted during the term.
Uploaded: 2026-04-05T16:23:03.589345+05:30
Duration: 1 min 45 s
Description: At the beginning of a term, the ratio of the number of boys in a school under 15 years to those over 15 years age was 5: 4. At the end of term,the ratio was 7:8 as of 20 boys had reached the age of 15 years during the term. Find the total number of‘Boys in the school, given that no boy left or was admitted during the term.

Solution

Let initial number of boys under 15 years and over 15 years are '5x' and '4x' respectively.

Now,

$$\frac{5x - 20}{4x + 20} = \frac{7}{8}$$

40x - 160 = 28x + 140

12x = 300

x = 25

Total boys in the exam = 5x + 4x = 9x = 225

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