Question

Two equal sums of money are lent at the same time at 8% and 7% per annum simple interest. The former is recovered 6 months earlier than the later and the amount in each case is Rs 2560. The sum and time for which the sums of money are lent out are 

(a) Rs 1500, 3.5 years and 4 years 

(b) Rs 2000, 3.5 years and 4 years 

(c) Rs 2000, 4 years and 5.5 years 

(d) Rs 3000, 4 years and 4.5 years

Answer 1

(b) Rs 2000, 3.5 years and 4 years

Let the sum be Rs x. 

∴ Rs x are lent at 8% for t years and Rs x are lent at 7% for \(\bigg(t+\frac{1}{2}\bigg)\)years.

∴ \(\frac{x\times{t}\times8}{100}\) + x = 2560       

⇒ 8tx + 100x = 256000    .......(i)

and \(\frac{x\times{(2t+1)}\times7}{2\times100}\) + x = 2560

⇒ \(\frac{14tx+7x+200x}{200}\) = 2560

⇒ 14tx + 207x = 512000    .....(ii)

Performing (i) × 7 – (ii) × 4, we get 

(56tx + 700x) – (56tx + 828x) = 256000 × 7 – 512000 × 4 

⇒ 700x – 828x = 1792000 – 2048000

⇒ 128x = 256000 ⇒ x = 2000 

Putting the value of x in (i), we get 

8 × t × 2000 + 100 × 2000 = 256000 

⇒ 16000t = 256000 – 200000 

⇒ 16000t = 56000 ⇒ t = \(\frac{56000}{16000} = \) 3.5 years.