Explanation

Given:

Time taken by A and B to complete the work = 12 days

Time taken by B and C to complete the work = 8 days

Time taken by C and A to complete the work = 6  days

Formulae used:

Time = Total work / Efficiency

Calculation:

Let us assume the total work is 1 unit.

⇒ A and B complete 1 unit work in 12 days → (A and B)'s 1 day's work = 1/12​

⇒ B and C complete 1 unit work in 8 days → (B and C)'s 1 day's work = 1/8​

⇒ A and C complete 1 unit work in 6 days → (A and C)'s 1 day's work = 1/6​

Adding everyone's 1 day's work:

$\Rightarrow 2(A+B+C)=(1/12+(1/8)+(1/6)$

⇒A+B+C=9/48​

= A, B, and C's 1 day's work = 9/48

⇒ B's 1 day's work = $(A+B+C)-(A+C)$

⇒ B's 1 day's work =(9/48)−(1/6) = 9-8 x/48 = 1/ 48 ​

​

⇒ B completes 1/48​ of the work in 1 day.

Therefore, B alone will take 48 days to complete the work.

Explanation

Given:

Time taken by 6 men to complete work= 10 days

Solution:

Time taken by 1 man = 6 x 10 = 6o hours

The time taken by 4 men to complete the work:

60/ 4 = 15 hours.

Explanation

Given:

• 12 people → Rs. 850 in 10 days

• 8 people → Rs. 340 in ? days

Let the required number of days be x.

Use the formula for compound proportion:

12×10​.850=8×x/340​

Step 2: Solve the equation

120./850​=8x/340​

Cross-multiply:

$$120 times 340 = 850 times 8x Rightarrow 40800 = 6800x Rightarrow x = frac{40800}{6800} = 6$$6800=6

Explanation

 Given:

6 men × 8 hours/day = total man-hours per day = 48 man-hours

They earn Rs. 720 per week

Now:

8 men × 6 hours/day = 48 man-hours per day — same total man-hours as before

So, since the total man-hours per day (and thus per week) are the same, the weekly earnings will also be the same.

Explanation

This is a classic inverse proportion problem:
More men → Less time required.

Given:

• 10 men take 40 days

• 20 men will take ? days

Since the number of men and the number of days are inversely proportional:

$$text{Men}_1 times text{Days}_1 = text{Men}_2 times text{Days}_2$$$$10 times 40 = 20 times x$$ $$400 = 20x Rightarrow x = frac{400}{20} = 20$$