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Inspired from Aatmanirbhar Bharat, Manoj and Sanoj started a restaurant. Manoj contributed Rs. 36000 for a certain time and Sanoj invested Rs. 45000 for the remaining time. They both continued this partnership for 36 months and if the ratio of total profit and profit earned by Manoj is 15 : 8, then find for what approximately time Manoj kept his money in the business ?

Inspired from Aatmanirbhar Bharat, Manoj and Sanoj started a restaurant. Manoj contributed Rs. 36000 for a certain time and Sanoj invested Rs. 45000 for the remaining time. They both continued this partnership for 36 months and if the ratio of total profit and profit earned by Manoj is 15 : 8, then find for what approximately time Manoj kept his money in the business ? Correct Answer 21 months

Given:

Contribution of Manoj = Rs. 36,000

Contribution of Sanoj = Rs. 45,000

Ratio of total profit to profit earned by Manoj = 15 : 8

Total time of investment = 36 months

Concept used:

Profit ∝ Investment
Profit ∝ Time
So, the ratio of profit is directly proportional to the product of investment and time.

Calculation:

Let the time for which Manoj invested the money be ‘x’ months

⇒ Time for which Sanoj invested the money = 36 – x months

Ratio of contribution of Manoj and Sanoj = 36000/45000

⇒ Ratio of contribution of Manoj and Sanoj = 4 : 5

 According to the concept mentioned above,

⇒ Ratio of Profit of Manoj to Sanoj = 4(x)/5(36 – x)

Let the total profit and Manoj’s profit be 15y and 8y

⇒ Total profit = Manoj’s Profit + Sanoj’s Profit

⇒ 15y = Sanoj’s Profit + 8y

⇒ Sanoj’s Profit = 15y – 8y = 7y

Ratio of profit of Manoj to Sanoj = 8y/7y

⇒ Ratio of profit of Manoj to Sanoj = 8 : 7

According to the question,

⇒ 4(x)/5(36 – x) = 8/7

⇒ 28x = 40(36 – x)

⇒ 28x = 1440 – 40x

⇒ 68x = 1440

⇒ x = 1440/68

⇒ x = 21.1 ≈ 21 months

∴ Manoj kept his money for 21 months. 

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