Question

A man spends 33.33% of his salary on cloth, 16.66% of the remaining on the study, 14.28% of the remaining on the rent of the house, and the remaining amount deposited in the bank. If he deposited the amount in the bank is Rs. 840. Find his total expenditure.
1. Rs. 924
2. Rs. 824
3. Rs. 786
4. Rs. 945

Answer 1

Correct Answer - Option 1 : Rs. 924

Given:

Expenditure on cloth = 33.33%

⇒ (1/3)

Expenditure on the study = 16.66% of the remaining

⇒ (1/6) of the remaining

Expenditure on the house = 14.28% of remaining

⇒ (1/7) of remaining

The remaining amount deposited in a bank = Rs. 840

Concept used:

Remaining of remaining:

Let a person spends x% percent on the cloth from his salary and y% of remaining on the study and he left of amount z.

Then [(100 -x)/100] × [(100 - y)/100] of his salary = z

Calculation:

Let his salary be Rs. p

According to the question,

p[1 - (1/3)] × [1 - (1/6)] × [1 - (1/7)] = 840

⇒ p[(3 - 1)/3] × [(6 - 1)/6]  × [(7 - 1)/7] = 840

⇒ p(2/3)(5/6)(6/7) = 840

⇒ (10/21)p = 840

⇒ p = 840 × (21/10)

⇒ p = 17640/10

⇒ p = Rs. 1764

Now his expenditure = total salary - saving

⇒ 1764 - 840

⇒ Rs. 924 

∴ His total expenditure is Rs. 924