A certain sum of money amounts to Rs 918 in 2 years and Rs 969 in 3.5 years at simple interest. What is the rate of interest (in %)?

Let sum of money = Rs. $$100x$$ and rate of interest = $$r\%$$

Amount under simple interest = $$P+\frac{P\times r\times t}{100}$$

In 2 years, sum amounts to Rs. 918

=> $$100x+\frac{100x\times r\times 2}{100}=918$$

=> $$100x+2rx=918$$ -----------(i)

Similarly, after 3.5 years, => $$100x+\frac{100x\times r\times 3.5}{100}=969$$

=> $$100x+3.5rx=969$$ ------------(ii)

Subtracting equation (i) from (ii),

=> $$1.5rx=969-918=51$$

=> $$rx=\frac{51}{1.5}=34$$ --------------(iii)

Substituting it in equation (i), => $$100x=918-2(34)=850$$

=> $$x=\frac{850}{100}=8.5$$

Substituting it in equation (iii), we get : $$r=\frac{34}{8.5}=4\%$$

=> Ans - (A)