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There are 40 boys in a PG. Due to some family reasons, 10 students leave PG. After this, the total expenses for the mess were decreased by Rs 30 while the average expenditure per head increased by Rs. 5. What was the original average expenditure of a boy in PG?

There are 40 boys in a PG. Due to some family reasons, 10 students leave PG. After this, the total expenses for the mess were decreased by Rs 30 while the average expenditure per head increased by Rs. 5. What was the original average expenditure of a boy in PG? Correct Answer Rs. 18

Given:

Total boys in PG = 40

Number of boys who leave PG = 10

Decrements in the expenditure of PG = Rs. 30 

Increment in the average expenditure of each person = Rs. 5 per person

Formula used:

Average = the sum of all numbers/total number

Calculation:

Total boys in PG = 40

Let the initial average expenditure of PG be Rs. x

The sum of their expenditure = 40 × x = Rs. 40x

Due to some family reason,

Now the total boys in PG = 40 - 10 = 30

Decrements in the expenditure of PG = Rs. 30 

So now the sum of their expenditure = Rs. (40x – 30)

Then now the average expenditure of each member = (40x – 30)/30

But there is an increment of Rs. 5 in the average expenditure of each person

Then,

⇒ x + 5 = (40x – 30)/30

⇒ 30x + 150 = 40x – 30

⇒ 10x = 180

⇒ x = 18

∴ The average initial expenditure of per person in PG is Rs. 18.

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