Ms Desh kept aside `40%` of her annual savings for a trip. Out of the remaining she gave `30%` to her son, `20%` to her mother and invested `15%` in a scheme. At the end she is left with ₹42000, besides the amount kept aside for the trip. What was her annual savings ?

Options

A. ₹240000
B. ₹180000
C. ₹120000
D. ₹200000

Answer

To find Ms. Desh's annual savings, we can break down the problem step by step.

### Step 1: Define the Total Annual Savings
Let Ms. Desh's total annual savings be represented as \( 100x \).

### Step 2: Calculate the Amount Set Aside for the Trip
Ms. Desh kept aside 40% of her annual savings for a trip. Therefore, the amount set aside for the trip is:
\[ \text{Amount for trip} = 40\% \text{ of } 100x = \frac{40}{100} \times 100x = 40x \]

### Step 3: Calculate the Remaining Amount After Setting Aside for the Trip
After setting aside the amount for the trip, the remaining amount is:
\[ \text{Remaining amount} = 100x - 40x = 60x \]

### Step 4: Calculate the Amount Given to Others
Out of the remaining amount, Ms. Desh gave:
- 30% to her son
- 20% to her mother
- 15% for investment

The total percentage given away is:
\[ 30\% + 20\% + 15\% = 65\% \]
Thus, the amount given away from the remaining \( 60x \) is:
\[ \text{Amount given away} = 65\% \text{ of } 60x = \frac{65}{100} \times 60x = 39x \]

### Step 5: Calculate the Amount Left After Giving Away
The amount left after giving away is:
\[ \text{Amount left} = 60x - 39x = 21x \]

### Step 6: Set Up the Equation Based on the Amount Left
According to the problem, Ms. Desh is left with ₹42,000 after all these transactions. Therefore, we can set up the equation:
\[ 21x = 42000 \]

### Step 7: Solve for \( x \)
To find \( x \), divide both sides of the equation by 21:
\[ x = \frac{42000}{21} = 2000 \]

### Step 8: Calculate the Total Annual Savings
Now we can calculate the total annual savings:
\[ \text{Total Annual Savings} = 100x = 100 \times 2000 = 200000 \]

### Final Answer
Thus, Ms. Desh's annual savings is ₹200,000.

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