Question

David invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs 3200 and the amount invested in Scheme C was 150% of the amount invested in Scheme A and 240% of the amount invested in Scheme B, what was the amount invested in scheme B ? 

(a) Rs 5000 

(b) Rs 6500 

(c) Rs 6000 

(d) Rs 8000

Answer 1

(a) Rs 5000.

Let x, y and z be the amounts invested in schemes A, B and C respectively. Then,

\(\bigg(\frac{x\times10\times1}{100}\bigg)\) + \(\bigg(\frac{y\times12\times1}{100}\bigg)\) + \(\bigg(\frac{z\times15\times1}{100}\bigg)\) = 3200

⇒ 10x + 12y + 15z = 320000         ......(i)

Given, Z = 240% of y = \(\frac{240}{100} \) x y = \(\frac{12}{5} \)y .......(ii)

and z = 150% of x = \(\frac{150}{100} \) x \(x = \frac{3}{2}x \)

⇒ x = \(\frac{2}{3} \)z = \(\frac{2}{3} \) x \(\frac{12}{5} \)y = \(\frac{8}{5} \)y            .....(iii)

∴ From (i), (ii) and (iii) we have

10 x \(\frac{8}{5} \)y + 12y + 15 x \(\frac{12}{5} \)y = 320000

⇒ 16y + 12y +36y = 320000 ⇒ 64y = 320000

⇒ y = \(\frac{320000}{64} \) = 5000.

∴ Sum invested in scheme B = Rs 5000.