Manu invested 15% of his monthly salary in the FD and 10% in PPF. 3/2...
Let, Manu’s monthly salary = Rs. x
∴ invested in FD = Rs. x × 15/100 = Rs. 0.15x
∴ invested in PPF = Rs. x × 10/100 = Rs. 0.1x
∴ spent on cloth = [x - (0.15x + 0.1x)] × 3/25 = 0.09x
∴ spent on food = [x - (0.15x + 0.1x + 0.09x)] × 3/11 = 0.18x
∴ spent on education = [x - (0.15x + 0.1x + 0.09x + 0.18x)] × 5/12 = 0.2x
∴ Remaining amount = x - (0.15x + 0.1x + 0.09x + 0.18x + 0.2x) = 0.28x
In case of simple interest,
Principal = Rs. 0.28x
Rate of interest = 10%
Time = 5 years
∴ Amount after 5 years,
⇒ 0.28x + 0.28x × 10 × 5/100
⇒ 0.42x
According to problem,
⇒ 0.42x = 16800
⇒ x = 16800/0.42
⇒ x = 40000
∴ Manu’s monthly salary = Rs. 40000
Manu invested 15% of his monthly salary in the FD and 10% in PPF. 3/2...
To solve this problem, we need to follow the given steps:
Step 1: Calculate the amount invested in FD and PPF.
- Manu invested 15% of his monthly salary in FD and 10% in PPF.
- Let's assume his monthly salary is 'x'.
- Amount invested in FD = 15% of x = 0.15x
- Amount invested in PPF = 10% of x = 0.10x
Step 2: Calculate the remaining amount after the investments in FD and PPF.
- Remaining amount = x - (0.15x + 0.10x)
= x - 0.25x
= 0.75x
Step 3: Calculate the amount spent on clothing.
- 3/25th of the remaining amount is spent on clothing.
- Amount spent on clothing = (3/25) * (0.75x)
= 9x/100
Step 4: Calculate the remaining amount after the clothing expenditure.
- Remaining amount = 0.75x - (9x/100)
= (75x/100) - (9x/100)
= 66x/100
= 0.66x
Step 5: Calculate the amount spent on food.
- 3/11th of the remaining amount is spent on food.
- Amount spent on food = (3/11) * (0.66x)
= 18x/55
Step 6: Calculate the remaining amount after the food expenditure.
- Remaining amount = 0.66x - (18x/55)
= (66x/100) - (18x/55)
= (330x/500) - (180x/500)
= 150x/500
= 0.3x
Step 7: Calculate the amount spent on education.
- 5/12th of the remaining amount is spent on education.
- Amount spent on education = (5/12) * (0.3x)
= 0.125x
Step 8: Calculate the remaining amount after the education expenditure.
- Remaining amount = 0.3x - 0.125x
= 0.175x
Step 9: Calculate the total amount after 5 years of investment in the scheme.
- The remaining amount is invested in a scheme offering 10% simple interest.
- After 5 years, the total amount is Rs. 16800.
- Let's assume the remaining amount is 'y'.
- Total amount after 5 years = y + (0.1y * 5)
= y + 0.5y
= 1.5y
- Given, 1.5y = 16800
- y = 16800 / 1.5
- y = 11200
Step 10: Calculate the monthly salary.
- The remaining amount after education expenditure is y = 11200.
- The remaining amount after the investments in FD, PPF, clothing, food, and education is 0.175x = 11200.
- x = 11200 / 0.175
- x = 64000
Therefore, Manu's monthly salary is Rs. 40000 (option 'A').