Select the correct answerA starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?Options6578

The profit share is directly proportional to the product of the invested capital and the time period for which it is invested.

Let's denote:

• the time period for which A's capital was invested as Ta (in months),
• the time period for which B's capital was invested as Tb (in months),
• A's capital as Ca,
• B's capital as Cb.

Given:

• Ta = 12 months (since A started the business and stayed for a year),
• Ca = Rs. 85,000,
• Cb = Rs. 42,500,
• The ratio of A's profit to B's profit = 3/1.

We can write the equation as follows:

(Ca * Ta) / (Cb * Tb) = 3/1

Substituting the given values into the equation:

(85000 * 12) / (42500 * Tb) = 3/1

Solving for Tb gives:

Tb = (85000 * 12) / (42500 * 3) = 8 months

So, B must have joined the business for 8 months.

To find out for how long B joins the business, we can use the concept of the ratio of investments and the ratio of profits.

Let's assume that B joins the business after x months.

The ratio of investments is given as 85,000 : 42,500, which simplifies to 17 : 8.

Since the profits are divided in the ratio of 3 : 1, we can set up the equation:

(17x) / (8(12 - x)) = 3/1

To solve this equation, we can cross-multiply:

3(8(12 - x)) = 1(17x)

Simplifying further:

24(12 - x) = 17x

Expanding:

288 - 24x = 17x

Bringing like terms together:

41x = 288

Dividing both sides by 41:

x = 288 / 41

Calculating this value:

x ≈ 7.024

Therefore, B joins the business for approximately 7 months.