Question : The monthly salary of a person was INR 75,000. He used to spend on Family Expenses (E), Taxes (T), and Charity (C), and the rest was 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 ratio of the savings of his earlier salary to that of his present salary is:
Option 1: 655 : 644
Option 2: 325 : 337
Option 3: 644 : 655
Option 4: 337 : 325
Correct Answer: 655 : 644
Solution :
Savings = Income − (E + T + C)
E = 0.60 × 75000 = 45000
T = 0.20 × 45000 = 9000
C = 0.15 × 9000 = 1350
Now, savings = 75000 − (45000 + 9000 + 1350) = 19650
When his salary was raised by 40%,
New Income = 1.40 × Old Income = 1.40 × 75000 = 105000
Also, new E = 0.60 × 105000 = 63000
New T = 0.30 × 63000 = 18900
New C = 0.20 × 18900 = 3780
⇒ New Savings = 105000 – (63000 + 18900 + 3780) = 19320
Now, the required ratio = $\frac{\text{Old Savings}}{\text{New Savings}}$ = $\frac{19650}{19320}$ = $\frac{655}{644}$
Hence, the correct answer is 655 : 644.
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