The amount of a certain sum in 3 years at simple interest at x% p.a. is Rs 5,472 and the amount of the same sum in 7years at the same rate, at simple interest is Rs 6,930. The value of x is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 7.2
The amount of a certain sum in 3 years at simple interest at x% p.a is Rs. 5,472.
The amount of the same sum is 71/2 i.e. 7.5 years at the same rate, at simple interest is Rs. 6,930.
Simple Interest, SI = (P × R × T)/100
Amount = P + SI (where P = Principal, R = Rate of interest per year, T = Time in years)
Let the sum be Rs. p.
According to the question -
p + (p × x × 3)/100 = 5472 ....(1
According to the question -
p + (p × x × 7.5)/100 = 6930 ....(2
(2) - (1) we get -
p + (p × x × 7.5)/100 - p - (p × x × 3)/100 = 6930 - 5472
7.5xp/100 - 3xp/100 = 1458
4.5xp/100 = 1458
xp = 145800/4.5
xp = 32400 ....(3
Putting xp = 32400 in (2
p + (p × x × 7.5)/100 = 6930
p + (32400 × 7.5)/100 = 6930
p = 6930 - (32400 × 7.5)/100
p = 6930 - 2430
p = 4500 ....(4
Putting p = 4500 in (3
x × 4500 = 32400
x = 32400/4500
x = 7.2