A started a business with a capital of Rs. 1,12,000. After 2 months, B joined the business with a capital of Rs. 80,000, and after another 2 months, C joined the business with a capital of Rs. 72,000. After 10 months from the start of the business, B withdraws Rs. 8,000 and C also withdraws Rs. 8,000. If B received Rs. 9,800 as his share in the profit at the end of a year, then the total profit was :

Given:

Capital of A = Rs. 1,12,000

Capital of B = Rs. 80,000

Capital of C = Rs. 72,000

Time before B joined = 2 months

Time before C joined = 4 months

Time B and C withdraw Rs. 8,000 each = 10 months

Share of B in profit = Rs. 9,800

Formula Used:

Profit share ratio = (Capital × Time)

Calculation:

Time for which A's capital was invested = 12 months

Time for which B's capital was invested = 10 months

Time for which C's capital was invested = 8 months

A's capital × Time = 112000 × 12 = 1344000

B's capital × Time (before withdrawal) = 80000 × 8 = 640000

B's capital × Time (after withdrawal) = (80000 - 8000) × 2 = 72000 × 2 = 144000

Total B's capital × Time = 640000 + 144000 = 784000

C's capital × Time (before withdrawal) = 72000 × 6 = 432000

C's capital × Time (after withdrawal) = (72000 - 8000) × 2 = 64000 × 2 = 128000

Total C's capital × Time = 432000 + 128000 = 560000

A, B and C profit ratio = 1344000 : 784000 : 560000

On simplification we get,

84 : 49 : 35

B's share in profit = Rs. 9800

⇒ 49 = 9800

⇒ 168 = 9800/49 × 168

= 33600

⇒ Total Profit = Rs. 33600

The total profit was Rs. 33600.