Question

A merchant gained 30% on 1/4
of his capital, lost 20% on 2/3 of his capital and made no gain no loss on the remainder. the gain/lose on the whole is

(a) loss of 35/6%
(b) gain of 55/6%
(c) no gain no loss
(d) gain of 30/6%​

Answer 1

Answer:

no gain no loss ok or 30/6

Answer 2

Step-by-step explanation:

$initial \: capital = 100$

$\frac{1}{4} of \: capital \: = \frac{1}{4} \times 100 = 25$

$gain 30\% = \frac{30}{100} \times 25 = \frac{30}{4} = \frac{15}{2}$

$\frac{2}{3} of capital = \frac{2}{3} \times 100 = \frac{200}{3}$

$loss \: 20\% = \frac{20}{100} \times \frac{200}{3} = \frac{40}{3}$

$gain \: = \frac{15}{2}$

$loss \: = \frac{40}{3}$

$total \: capital = 100 + \frac{15}{2} - \frac{40}{3} \\ \\ = \frac{600 + 40 - 80}{6} = \frac{565}{6}$

$loss = 100 - \frac{565}{6} = \frac{600 - 565}{6} = \frac{35}{6}$

Loss 35/6% Answer