A father divides a loan of Rs. 2,60,200 between his son and daughter so that the amount of son after 7 years is equal to the amount of daughter after 9 years, the interest being compounded at 4% pa.
1. 135200, 125000
2. 140000, 135000
3. 141500, 135400
4. 150000, 145000
1. 135200, 125000
2. 140000, 135000
3. 141500, 135400
4. 150000, 145000
Correct Answer – Option 1 : 135200, 125000
Given:
Loan amount = Rs. 2,60,200
Rate of interest = 4% pa
Formula used:
Amount = Principal × [1 + r/100]n
Calculations:
Let the first part be x
The second part = (260200 – x)
According to the question,
x(1 + 4/100)7 = (260200 – x)(1 + 4/100)9
⇒ x/(260200 – x) = (1 + 4/100)9/(1 + 4/100)7
⇒ x/(260200 – x) = 26/25 × 26/25
⇒ x/(260200 – x) = 676/625
⇒ 625x = 676 × 260200 – 676x
⇒ 1301x = 676 × 260200
⇒ x = (676 × 260200)/1301
⇒ x = 135200
Second part = 260200 – x
⇒ 260200 – 135200
⇒ 125000
∴ the two parts are 135200 and 125000.