A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of the interest be 10% compounded annually, then the value of each installment is:

Answer: Option A

Let X = equal installment at the end of one year( rate% annually) .
Now 1st year,
P =210,
Interest = $$\frac{\text{PTR}}{100}$$  = 210 * 0.1 = 21.
Let X is to be paid as an equal installment.
Now, at the beginning of 2nd year,
P = 210 + 21 - X,
Interest at the end of 2nd year,
= (231 - X) * 0.1 = 23.1 - 0.1X.
Hence,total installment,
2X = 210 + 21 + 23.1 - 0.1X,
X = $$\frac{\text{254}\text{.1}}{2.1}$$  = 121.