A sum of Rs 7500 is divided into two parts. The simple interest on first part at the rate of 12% per annum is equal to the simple interest on second part at the rate of 18%. What is the interest (in Rs) on each part for one year?

Let sum invested for 12% = Rs. $$100x$$ and sum invested for 18% = Rs. $$(7500-100x)$$

Time period = 1 year

=> Simple interest = $$\frac{P\times R\times T}{100}$$

According to ques,

=> $$\frac{100x\times12\times1}{100}=\frac{(7500-100x)\times18\times1}{100}$$

=> $$12x=(75-x)\times18$$

=> $$12x=1350-18x$$

=> $$12x+18x=30x=1350$$

=> $$x=\frac{1350}{30}=45$$

$$\therefore$$ Interest for each part = $$\frac{100\times45\times12\times1}{100}$$

= Rs. $$540$$

=> Ans - (D)