If the compound interest on a sum for 2 years at per annum is RS. 340, then the simple interest on the same sum at the same rate for the same period of time is

The question as printed leaves out the rate. Without it, every option can be made to fit some rate, so the answer depends on the rate in the standard version of this problem, which is 12.5% per annum. Keep that assumption in mind while you work it out.

For two years, CI = P(2r + r²) and SI = 2Pr. So CI minus SI = Pr², and SI = CI x 2/(2 + r), with r as a decimal. At r = 0.125, SI = 340 x 2/2.125 = 320.

Check: P = 1280 gives CI = 1280 x (1.125² - 1) = 340 and SI = 2 x 1280 x 0.125 = 320.

• A (310), C (330), D (335): each would need a different rate to produce CI of 340. For example, SI of 330 needs a rate of about 6%, not 12.5%. At 12.5%, only 320 reproduces CI of 340.

Core concept: the gap between CI and SI over two years is the Pr² term, which is why the two differ by a small amount. This is basic quantitative aptitude for Prelims and also shows up in Mains economy questions on compounding.

Trap: treating the question as solvable without a rate, or using 12.5 directly in the formula instead of 0.125.