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In a mess, there were 40 inmates. As 5 more have joined, the average expenses were decreased by Rs. 1, but the total expenses increased by Rs. 55. What was the total initial expense of the mess?

In a mess, there were 40 inmates. As 5 more have joined, the average expenses were decreased by Rs. 1, but the total expenses increased by Rs. 55. What was the total initial expense of the mess? Correct Answer Rs. 800

Given:

In a mess, there were 40 inmates.

As 5 more have joined, the average expenses were decreased by Rs. 1, but the total expenses increased by Rs. 55.

Concept Used:

Total = Average × Number of observations

Calculation:

Let, initially average expense was x

⇒ Total expense was 40x

At present total number of inmates = (40 + 5)

⇒ 45

Average expense = (x - 1)

Total present expense = 45 × (x - 1)

⇒ (45x - 45)

Accordingly,

45x - 45 = 40x + 55

⇒ 5x = 100

⇒ x = 20

Initially total expenses was 20 × 40 = 800

∴ The total initial expense of the mess was Rs. 800.

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