Rohan and Sohan started business with Rs. 2000 and Rs. 3000 respectively. After six-month Rohan withdrew x% of his investment and Rajni rep… — Answer & Discussion

Rohan and Sohan started business with Rs. 2000 and Rs. 3000 respectively. After six-month Rohan withdrew x% of his investment and Rajni replace Sohan with x% of Sohan’s Capital. After 1 year Rajni’s share of profit is Rs. 1200 out of the total profit of Rs. 7400. Find the value of x?

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Discussion 1

CCommunity05 Jun 2019

For the first 6 months,

Investment of Rohan = Rs. 2000

Investment of Sohan = Rs. 3000

Investment of Rajni = Rs. 0

For the next 6 months,

Investment of Rohan = Rs. (2000 - 2000 × x/100) = Rs. (2000 - 20x)

Investment of Sohan = Rs. 0

Investment of Rajni = Rs. 3000 × x/100 = Rs. 30x

∴ Effective ratio of their investments,

⇒ [2000 × 6 + (2000 - 20x) × 6] ? 3000 × 6 ? 30x × 6

⇒ 24000 - 120x ? 18000 ? 180x

⇒ 400 - 2x ? 300 ? 3x

According to problem,

$(\Rightarrow \frac{{3x}}{{400 - 2x + 300 + 3x}} = \frac{{1200}}{{7400}})$

⇒ 3x/(700 + x) = 6/37

⇒ 111x = 4200 + 6x

⇒ 105x = 4200

⇒ x = 40