Question

Two equal sums of money are learnt to A and B for 3 years at 4% and 6% simple interest respectively if B paid 468 rupees more than A find the sum lent each

Answer 1

Principal Amount of Money

We need to find the Principal amount of money

Solution:

Amount of money lent to A = Amount of money Lent to B = P

Amount = Principal + Simple Interest =Principal + $\frac { P \times R \times T} {100}$

Amount of A =

$$A_A = P + \frac { P \times R \times T} {100} = P + \frac { P \times 4 \times 3} {100}$$

$$A_A = P + \frac {12P} {100} = \frac {112P}{100}$$

Amount of B =

$$A_B = P + \frac { P \times R \times T} {100} = P + \frac { P \times 6 \times 3} {100}$$

$$= P + \frac {18P}{100} = \frac {118P} {100}$$

B paid 468 rupees more than A

means, Amount of B = Amount of A + 468

$$A_B = A_A + 468$$

$$\frac {118P}{100} = \frac {112P}{100} + 468$$

$$\frac {118P}{100} - \frac {112P}{100} = 468$$

$$\frac {118P - 112P} {100} = 468$$

$$\frac {6P} {100} = 468$$

$$6P = 46800$$

$$P = 7800$$

Answer:

The sum lent each = 7800 rupees