A sum of ₹27,000 is divided into two parts A and B such that the simple interest at the rate of 15% p.a. on A and after two years and four years, respectively, is equal. The total interest (in ₹) received together from A and B is:

10,800

Total Principal = Rs 27000 ( X + Y)

It is divided into parts .

First part at 15% in 2 years at Principal ( X)

First part at 15% in 4 years at Principal ( Y)

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

ATQ

Interest_{1  =}  Interest ₂

\(\frac{X ×15×2}{100}\) =\(\frac{Y×15×4}{100}\)

2X =  4Y

X :  Y

2: 1

ATQ

3  part =  27000

1 part = 9000

Principal ( X) = 2× 9000 =  Rs 18000

Principal ( Y) = 1× 9000 =  Rs 9000

Total Interest = Rs  Interest₁  + Interest ₂

                       = \(\frac{18000×15× 2 }{100}\) + \(\frac{9000×15× 4 }{100}\)

                        = 5400+ 5400

                        = Rs 10800