A, B and C can do a work in 8, 10 and 12 days, respectively. After completing the work together, they received `5,550. What is the share of B (in `) in the amount received?

The correct answer is ₹1,800.

In work-and-wages problems, the total payment is divided among workers in proportion to their individual efficiencies (i.e., the rate at which each person works). A worker who works faster contributes more and thus earns a larger share.

Step 1: Find the individual efficiencies (work done per day)

Efficiency is simply the fraction of total work one person completes in a single day.

A's efficiency = \frac{1}{8} of the work per day

B's efficiency = \frac{1}{10} of the work per day

C's efficiency = \frac{1}{12} of the work per day

Step 2: Express the ratio of efficiencies

The ratio of their shares = A : B : C = \frac{1}{8} : \frac{1}{10} : \frac{1}{12}

To eliminate fractions, multiply each term by the LCM of 8, 10, and 12.

Finding LCM(8, 10, 12):
8 = 2³,   10 = 2 × 5,   12 = 2² × 3
LCM = 2³ × 3 × 5 = 120

Multiplying each fraction by 120:

A : \frac{120}{8} = 15

B : \frac{120}{10} = 12

C : \frac{120}{12} = 10

So the simplified ratio of shares is A : B : C = 15 : 12 : 10

Step 3: Find the total number of ratio parts

Total parts = 15 + 12 + 10 = 37

Step 4: Calculate B's share

B's share = \frac{12}{37} × ₹5,550

= 12 × \frac{5550}{37} = 12 × 150 = ₹1,800

Verification:

A's share = \frac{15}{37} × 5550 = 15 × 150 = ₹2,250
B's share = ₹1,800
C's share = \frac{10}{37} × 5550 = 10 × 150 = ₹1,500

Total = 2,250 + 1,800 + 1,500 = ₹5,550 ✓

Therefore, B's share is ₹1,800.