A person invests an amount at 5% rate of interest in first year and at 10% in second year. He receives an amount of Rs. 1155 at the end of two years. Calculate principal amount invested.
1. Rs. 2300
2. Rs. 1800
3. Rs. 1000
4. Rs. 1200
1. Rs. 2300
2. Rs. 1800
3. Rs. 1000
4. Rs. 1200
Correct Answer – Option 3 : Rs. 1000
Given:
A= Rs. 1155
R = 5% and 10%
N = 2 years
Formula used:
I = PRN / 100
Where P = Principal amount, R = Rate of interest in %, N = Number of years, I = Interest earned
A = P + I
Where A = Amount received
Calculation:
A = P + I
⇒ A = P + (PRN / 100)
⇒ A = P (1 + RN / 100)
⇒ A = P (1 + (5 × 1 / 100)) × (1 + (10 × 1 / 100)) [∵ Interest was 5% and 10% in 1st and 2nd year]
⇒ 1155 = P × (21 / 20) × (11 / 10)
⇒ P = (1155 × 20 × 10) / (21 × 11)
⇒ P = 5 × 20 × 10
⇒ P = Rs. 1000
∴ Principal amount invested Rs. 1000.
Short Trick
If we take 100 as the principle.
After the first year the principle increased to 105.
And after second year, the amount increased to 115.5.
If he received 1155 as amount.
Then, 1 unit is 10
Then, 100 unit is 1000.