Question : A man spent 30% of his monthly income on rent. He spent 15% of the remaining amount on food. 35% of the amount now left was used for all other expenses. If Rs. 1,62,435 was left with him, then his monthly income was:
Option 1: Rs. 4,80,000
Option 2: Rs. 4,20,000
Option 3: Rs. 3,60,000
Option 4: Rs. 5,40,000
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Correct Answer: Rs. 4,20,000
Solution :
Let the salary be $100x$.
Expense on food $= \frac{30}{100} \times 100x = 30x$
Remaining $= (100x-30x) = 70x$
Expense on rent $= 15\% \times 70x = \frac{15}{100}\times 70x = \frac{1050x}{100}=10.5x$
Remaining $= (70x-10.5x) = 59.5x$
Other expense $= 35\% \times 59.5x = \frac{35}{100} \times 59.5 = \frac{2082.5}{100} = 20.825x$
We know that,
Salary = expense on food + rent + other expenses + savings
$100x = 30x+10.5x+20.825x+162435$
⇒ $100x= 61.325x+162435$
⇒ $38.675x = 162435$
$\therefore x= 4200$
$\therefore$ Total Salary $= 4200 \times 100 = 420000$
Hence, the correct answer is Rs. 4,20,000.
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