At the beginning of a year, the ratio of the number of boys of age up

1.	At the beginning of a year, the ratio of the number of boys of age up to 16 years to those over 16 years was 8 : 5. At the end of the year, the ratio became 6 : 7 as 40 boys had reached the age of 16 years by then. What is the total number of boys in the school if no boy left or got admission during the year?1. 2732. 2603. 2864. 247
Answer» Correct Answer - Option 2 : 260 Given: Ratio at the beginning of the year = 8 : 5 Ratio at the end of the year = 6 : 7 Number of boys reached the age of 16 years by the end of year = 40 Calculation: Let the number of boys having age upto 16 years and those over the age of 16 years at the beginning of year be 8x and 5x respectively. As by the end of year 40 boys had reached the age of 16 years, then Number of boys having age upto 16 years = 8x - 40 Number of boys having age more than 16 years = 5x + 40 (8x - 40)/(5x + 40) = 6/7 ⇒ 56x - 280 = 30x + 240 ⇒ 56x - 30x = 240 + 280 ⇒ 26x = 520 ⇒ x = 20 Total number of boys in the school = 8x + 5x ⇒ 13x ⇒ 13 × 20 ⇒ 260 ∴The total number of boys in the school is 260.

At the beginning of a year, the ratio of the number of boys of age up to 16 years to those over 16 years was 8 : 5. At the end of the year, the ratio became 6 : 7 as 40 boys had reached the age of 16 years by then. What is the total number of boys in the school if no boy left or got admission during the year?1. 2732. 2603. 2864. 247

Answer» Correct Answer - Option 2 : 260

Given:

Ratio at the beginning of the year = 8 : 5

Ratio at the end of the year = 6 : 7

Number of boys reached the age of 16 years by the end of year = 40

Calculation:

Let the number of boys having age upto 16 years and those over the age of 16 years at the beginning of year be 8x and 5x respectively.

As by the end of year 40 boys had reached the age of 16 years, then

Number of boys having age upto 16 years = 8x - 40

Number of boys having age more than 16 years = 5x + 40

(8x - 40)/(5x + 40) = 6/7

⇒ 56x - 280 = 30x + 240

⇒ 56x - 30x = 240 + 280

⇒ 26x = 520

⇒ x = 20

Total number of boys in the school = 8x + 5x

⇒ 13x

⇒ 13 × 20

⇒ 260

∴The total number of boys in the school is 260.