A person invested a certain amount at a rate of 12% simple interest and another amount at a rate of 10% simple interest. He received an annual interest of Rs 130. However, if he had interchanged the amounts invested, he would have received Rs 4 more as interest. How much did he invest at the rate of 12% simple interest originally?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. Rs.500.
Let the amount invested on 12% and 10% rates be x and y respectively.
SI = PRT/100
where P is principal, R is rate and T is time.
According to the given question,
x × 12 × 1/100 + y × 10 × 1/100 = 130
⇒ 12x + 10y = 13000
⇒ 6x + 5y = 6500 ...(i)
Also, y × 12 × 1/100 + x × 10 × 1/100 = 134
⇒ 12y + 10x = 13400
⇒ 5x + 6y = 6700 ...(ii)
Multiplying equation (i) by 6 and equation (ii) by 5,
(i) ⇒ 36x + 30y = 39000 ...(iii)
(ii) ⇒ 25x + 30y = 33500 ...(iv)
Subtracting equation (iv) from equation (iii),
⇒ 11x = 5500
⇒ x = 500