A sum of Rs36,000 is divided into two parts, A and B, such that the simple interest at the rate of 15% p.a. on A and B after two years and four years, respectively, is equal. The total interest ( in Rs) received from A is :
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 7,200.
We know that,
S.I. = (P × R × T)/100
here, S.I. = Simple Interest, P = Principal, R = rate and T = Time
Let Principle for A be Rs. P
Then principal for B = 36,000 - P
Simple interest for A = (P × 15 × 2)/100 = 30P/100 = 0.3P
Simple interest for B = [(36,000 - P) × 15 × 4]/100
⇒ 0.6 × (36,000 - P) = 21600 - 0.6P
Now, simple interest of A in 2 years = simple interest for B in 4 years.
0.3P = 21600 - 0.6P
⇒ 0.3P + 0.6P = 21600
⇒ 0.9P = 21600
⇒ P = 21600/0.9
⇒ P = 24000
Then,
Simple interest of A in two years = 0.3P = 0.3 × 24000 = Rs.7200