Question : The monthly salary of a person was INR 50,000. He used to spend on Family expenses (E), Taxes (T), and Charity (C), and the rest were his savings. E was 60% of the income. T was 20% of E, and C was 15% of T. When his salary was raised by 40%, he maintained the percentage level of E, but T became 30% of E and C became 20% of T. The difference between the two savings (in INR) is:
Option 1: 128
Option 2: 220
Option 3: 130
Option 4: 250
Correct Answer: 220
Solution :
Monthly salary = INR 50,000
E = 60% of income
T = 20% of E
C = 15% of T
After the salary was raised by 40%,
E = 60% of income
T = 30% of E
C = 20% of T
Let the initial salary be $1000x$.
E = 60% of $1000x$ = $600x$
T = 20% of $600x$ = $120x$
C = 15% of $120x$ = $18x$
Total expense $=600x + 120x + 18x = 738x$
Initial savings $=1000x - 738x = 262x$
After the salary was raised by 40%,
New salary = $1000x + 1000x$ × 40% = $1400x$
New E = 60% of $1400x$ = $840x$
New T = 30% of $840x$ = $252x$
New C = 20% of $252x$ = $50.4x$
New Total expense $=840x + 252x + 50.4x = 1142.4x$
New savings $=1400x - 1142.4x = 257.6x$
Difference in savings $=262x - 257.6x = 4.4x$
As $1000x$ = INR 50,000
So, $x$ = 50
Difference in savings = $4.4x$ = 4.4 × 50 = INR 220
$\therefore$ The difference between the two savings is INR 220.
Hence, the correct answer is 220.
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