The amount of a certain sum in 3 years at simple interest at x % p.a. is ₹5,472 and the amount of the same sum in 7(1/2) years at the same rate, at simple interest is ₹6,930. The value of x is:

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 ∴ The value of x is 7.2.