Question

there were 40 members in a certain hotel. if 10 members are more admitted the expenses of the mess was increase by Rs. 50 per month while the average expenditures per head diminished by Rs. 3. the Original monthly expenses are.

Answer 1

plz mark brainliest amswer

Answer 2

The original monthly expenses = Rs. 800

Given :

• There were 40 members in a certain hotel.

• If 10 members are more admitted the expenses of the mess was increase by Rs. 50 per month while the average expenditures per head diminished by Rs. 3

To find :

The original monthly expenses

Solution :

Step 1 of 2 :

Form the equation to find original monthly expenses

Let the original monthly expenses = Rs. x

Since there were 40 members in a certain hotel

∴ Average expenditures per head = Rs. x/40

If 10 members are more admitted then total number of members = 40 + 10 = 50

When total number of members is 50 expenses of the mess was increase by Rs. 50 per month

So new total expenses will be = Rs. (x + 50)

∴ New average expenditures per head

= Rs. (x + 50)/50

By the given condition

$\displaystyle \sf \frac{x}{40} - \frac{x + 50}{50} = 3$

Step 2 of 2 :

Calculate original monthly expenses

$\displaystyle \sf \frac{x}{40} - \frac{x + 50}{50} = 3$

$\displaystyle \sf{ \implies } \frac{5x - 4(x + 50)}{200} = 3$

$\displaystyle \sf{ \implies } \frac{5x - 4x - 200}{200} = 3$

$\displaystyle \sf{ \implies } x - 200 = 3 \times 200$

$\displaystyle \sf{ \implies } x - 200= 600$

$\displaystyle \sf{ \implies } x = 600 + 200$

$\displaystyle \sf{ \implies } x = 800$

Hence original monthly expenses = Rs. 800

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