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A sum of money amounts to Rs. 5580 at R% per annum simple interest in 6 years. The same sum will amount to Rs. 5130 at R/2% per annum simple interest in 7 years. What will be the simple interest on the same sum at 2R% per annum in 10 years?

A sum of money amounts to Rs. 5580 at R% per annum simple interest in 6 years. The same sum will amount to Rs. 5130 at R/2% per annum simple interest in 7 years. What will be the simple interest on the same sum at 2R% per annum in 10 years? Correct Answer Rs. 3600

Let the sum of money be Rs. ‘P’

∵ Simple interest = (Principal × Rate × Time)/100

Amount at R% in 6 years = P + (P × R × 6)/100

⇒ P + 6PR/100 = 5580      ----(1)

Amount at R/2% in 7 years = P + (P × R/2 × 7)/100

⇒ P + 7PR/200 = 5130      ----(2)

Subtracting (2) from (1), we get,

⇒ 6PR/100 – 7PR/200 = 5580 – 5130

⇒ PR/40 = 450

⇒ PR = 18000

∴ Simple interest at 2R% in 10 years = (P × 2R × 10)/100 = PR/5 = 18000/5 = Rs. 3600

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