A man invests an amount of ₹1,05,750 at simple interest in the name of his son, daughter and his wife in such a way that they get the same interest after 3, 4 and 5 years, respectively.If the rate of interest is 5% per annum, then the amount invested for the wife is:

₹27,000

Let share of Son , Daughter and wife = A , B  & C.

Simple interest in each case is same .

We know ,

Simple Interest = \(\frac{Principal ×Rate × Time }{100}\)

\(\frac{A ×5× 3 }{100}\) = \(\frac{B ×5× 4 }{100}\) = \(\frac{C ×5×5 }{100}\)

3A = 4B = 5C

Ratio of share of A , B & C = 20 : 15 : 12

( 20 + 15 + 12 )x = 105750

47x = 105750

x = \(\frac{105750 }{47 }\) = 2250

Share of wife = 12 × 2250 = Rs. 27000