Question

5. Sudhir, a very clever businessman, started off a
business with very little capital. In the first year,
he earned a profit of 50% and donated 50% of the
total capital (initial capital + profit) to a charitable
organisation. The same course was followed in the
2nd and 3rd years also. If at the end of three years,
he is left with 33,750, then find the amount donated
by him at the end of the 2nd year.​

Answer 1

Solution :-

Let us assume that, Sudhir started his business with capital Rs. 100x In first year .

First Year :-

So,

→ Profit in first year = 50% of 100x = (50 * 100x)/100 = Rs. 50x .

then,

→ Total capital at the end of 1 year = initial capital + profit = 100x + 50x = Rs. 150x

now,

→ Capital donated by Sudhir at the end of 1st year = 50% of 150 = (50 * 150x)/100 = Rs. 75x .

So,

→ Capital for second year = 150x - 75x = Rs. 75x

Second Year :-

→ Total capital = Rs. 75x

→ Profit = 50% of 75x = (50 * 75x)/100 = Rs. 37.5x

So,

→ Total capital at the end of 2 year = initial capital + profit = 75x + 37.5x = Rs. 112.5x

now,

→ Capital donated by Sudhir at the end of 2nd year = 50% of 112.5x = (50 * 112.5x)/100 = Rs. 56.25x -------- Eqn.(1)

So,

→ Capital for third year = 112.5x - 56.25x = Rs. 56.25x

Third Year :-

→ Total capital = Rs. 56.25x

→ Profit = 50% of 56.25x = (50 * 56.25x)/100 = Rs. 28.125x

So,

→ Total capital at the end of 3rd year = initial capital + profit = 56.25x + 28.125x = Rs. 84.375x

now,

→ Capital donated by Sudhir at the end of 3rd year = 50% of 84.375x = (50 * 84.375x)/100 = Rs. 42.1875x

So,

→ Capital after donated at the end third year = 84.375x - 42.1875x = Rs. 42.1875x

A/q,

→ 42.1875x = 33750

→ x = 800

therefore, putting value of x in Eqn.(1) we get,

→ Capital donated by Sudhir at the end of 2nd year = 56.25x = 56.25 * 800 = Rs. 45,000 (Ans.)

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