Out of his monthly income, A spends 50\% on rent, 20\% of the remaining on food, 10\% on travelling, and saves the rest amounting to Rs 10800. If B's monthly income is 25\% less than A's, what is 60\% of B's monthly income (in Rs)?

Question

Accepted Answer

**Solution:**

1. Let A's monthly income be $ x $.

2. A spends 50\% on rent, so remaining income after rent:
   $$
   x - 0.5x = 0.5x
   $$

3. A spends 20\% of the remaining on food:
   $$
  $ 20\% \text{ of } 0.5x = 0.2 \times 0.5x = 0.1x$
   $$
   Remaining after food:
   $$
   0.5x - 0.1x = 0.4x
   $$

4. A spends 10\% on travelling (of total income):
   $$
   $10\% \text{ of } x = 0.1x$
   $$

5. Amount saved by A is the rest:
   $$
  $ \text{Savings} = x - (\text{rent} + \text{food} + \text{travelling}$)
   $$
   $$
   = x - (0.5x + 0.1x + 0.1x) = x - 0.7x = 0.3x
   $$

6. Given savings = Rs 10800, so:
   $$
   $0.3x = 10800 \implies x = \frac{10800}{0.3} = 36000$
   $$

7. B's monthly income is 25\% less than A's:
   $$
   $\text{B's income} = 36000 - 0.25 \times 36000 = 36000 \times 0.75 = 27000$
   $$

8. Required value is 60\% of B's income:
   $$
   $0.6 \times 27000 = 16200$
   $$

**Note:** The options do not include Rs 16200, so let's re-check step 4.

Step 4 says A spends 10\% on travelling, but the question states "10\% on travelling" without specifying if it is on remaining or total income. The question states "10\% on travelling" after spending on food which was 20\% of the remaining. Usually, such questions imply 10\% of the remaining after food.

Let's consider 10\% of the remaining after food:

Remaining after food = 0.4x

Travelling expense = 10\% of 0.4x = 0.1 \times 0.4x = 0.04x

Now, total expenses:

Rent = 0.5x
Food = 0.1x
Travelling = 0.04x

Total expenses = 0.5x + 0.1x + 0.04x = 0.64x

Savings = x - 0.64x = 0.36x

Given savings = 10800

$$
$0.36x = 10800 \implies x = \frac{10800}{0.36} = 30000$
$$

$B's income = 75\% of A's income = 0.75 \times 30000 = 22500$

60\% of B's income = $0.6 \times 22500$ = 13500

This matches option (b).

**Answer:** Rs 13500

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