Question : Aman gave 30% of his monthly income to his father and of the remaining income he gave 30% to his daughter and 25% to his wife. Aman invested the amount of money remaining from his monthly income equally in three schemes. If he invested INR 42,000 in each scheme, what is Aman's monthly income (in thousands)?
Option 1: 300
Option 2: 400
Option 3: 200
Option 4: 500
Correct Answer: 400
Solution :
Let's denote Aman's monthly income as $x$
Amount given to his father = 30 % of $x$ = 0.30 $x$
Amount remaining income = $x$ − 0.30 × $x$ = 0.70 $x$
The amount given to His daughter = 30 % of 0.70 $x$ = 0.30 × 0.70 × $x$
= 0.21 $x$
The amount is given to his wife = 25 % of 0.70 $x$ = 0.25 × 0.70 × $x$ = 0.175 $x$
Amount Remaining = 0.70 $x$ – (0.21 $x$ + 0.175 $x$) = 0.70 – 0.385 = 0.315 $x$
Amount invested in scheme = 3 × 42000 = 126000
Now, according to the question
0.315 $x$ = 126,000
⇒ $x$ = $\frac{126000}{0.315}$ = 400,000 (400 thousands)
Hence, the correct answer is 400.
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