**Ques - Pratibha invests an amount of Rs. 15,860 in the names of her three daughters A, B and C in such a way that they get the same interest after 2, 3 and 4 years respectively. If the rate of simple interest is 5% p.a., then the ratio of the amounts invested among A, B and C will be :**

**(a) 5 : 10 : 12**

**(b) (1/10) : (1/15) : (1/20) **

**(c) 6 : 7 : 8**

**(d) 6 : 5 : 4**

**Solution - **

Given,

For A,

P = P1

T = 2 years

R = 5%

So,

S.I. = (P×R×T) / 100

S.I. = (P1 × 5 × 2) / 100

**S.I. = 10P1/100**

Now,

For B,

P = P2

T = 3 years

R = 5%

So,

S.I. = (P×R×T) / 100

S.I. = (P2 × 5 × 3) / 100

**S.I. = 15P2/100**

For C,

P = P3

T = 4 years

R = 5%

So,

S.I. = (P×R×T) / 100

S.I. = (P3 × 5 × 4) / 100

**S.I. = 20P3 / 100**

Thus,

10P1/100 = 15P2/100 = 20P3 / 100

10P1 = 15P2 = 20P3

P1 : P2 : P3 = (1/10) : (1/15) : (1/20)

Therefore,

**The ratio of the amounts invested among A, B and C will be (1/10) : (1/15) : (1/20).**

Hence,

The correct answer is option **(b) (1/10) : (1/15) : (1/20).**

Thank You