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Samson invested Rs.3750 in business and after some time Mandeep also joined him and invested Rs.3250. At the end of the year, Mandeep received Rs.2600 profit out of Rs.7100. After how much time did Mandeep join the business?

Samson invested Rs.3750 in business and after some time Mandeep also joined him and invested Rs.3250. At the end of the year, Mandeep received Rs.2600 profit out of Rs.7100. After how much time did Mandeep join the business? Correct Answer None of these

Given:

The investment of Samson = Rs.3750 for 12 months

After some time Mandeep also joined him and invested Rs.3250

Mandeep’s profit = Rs.2600

Total profit = Rs.7100

Concept:

The ratio of the capital equals to the ratio of the profit.

Formula used:

Total capital = investment × time of investment

Calculation:

The investment of Samson = Rs.3750 for 12 months

Suppose Mandeep invested Rs.3250 for x months

Then the ratio of their capital = Samson’s capital ∶ Mandeep’s capital

⇒ 3750 × 12 ∶ 3250 × x

⇒ 180 ∶ 13x

Mandeep’s profit = Rs.2600

Then Samson’s profit = 7100 – 2600 = Rs.4500

Now the ratio between their profit = Samson’s profit ∶ Mandeep’s profit

⇒ 4500 ∶ 2600 = 45 ∶ 26

The ratio of the capital equals to the ratio of the profit then

⇒ (180/13x) = 45/26

⇒ 45x = 360

⇒ x = 8

Mandeep’s investment time = 8 months

So he invested after = 12 – 8 = 4 months

∴ Mandeep joined the business after 4 months

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