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85 apples are to be distributed in a class consisting of boys and girls. If each boy gets 5 apples, then each girl will get 7 apples, and if each boy gets 4 apples, then each girl will get 9 apples. How many students are there in the class?

85 apples are to be distributed in a class consisting of boys and girls. If each boy gets 5 apples, then each girl will get 7 apples, and if each boy gets 4 apples, then each girl will get 9 apples. How many students are there in the class? Correct Answer 15

Let the number of boys be ‘x’ and number of girls be ‘y’.

So, total number of students in the class = x + y

If each boy gets 5 apples, then each girl will get 7 apples.

According to question:

5x + 7y = 85 ______ (i)

And, if each boy gets 4 apples, then each girl will get 9 apples.

4x + 9y = 85 ______ (ii)

Equating equation (i) and (ii), we get:

5x + 7y = 4x + 9y

⇒ 5x – 4x = 9y – 7y

⇒ x = 2y

Putting the value of ‘x’ in equation (i), we get:

5(2y) + 7y = 85

⇒ 10y + 7y = 85

⇒ 17y = 85

⇒ y = 85 ÷ 17

⇒ y = 5

As x = 2y and y = 5

The value of x = 2 × 5 = 10

Therefore, total number of students in the class = x + y = 10 + 5 = 15

Hence, ‘15’ is the correct answer.

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