Explanation

Let's calculate the total man-hours required to complete the work:

39 persons * 5 hours/day * 12 days = 2340 man-hours

If 30 persons work 6 hours a day:

Let x be the number of days they need to complete the work:

30 persons * 6 hours/day * x days = 2340 man-hours

180x = 2340

x = 13

Explanation

After 10 days: 150 men had food for 35 days.

Suppose 125 men had food for x days.

Now, Less men, More days (Indirect Proportion)

 125 : 150 :: 35 : x        125 x x = 150 x 35

 x =         150 x 35

125

 x = 42.

Explanation

Let's calculate the total pump-hours required to empty the tank:

3 pumps * 8 hours/day * 2 days = 48 pump-hours

If 4 pumps need to empty the tank in 1 day:

Let x be the number of hours they need to work:

4 pumps * x hours/day * 1 day = 48 pump-hours

4x = 48

x = 12

Explanation

Probability = 5C2/7C2 = 10/21

Total number of balls = 2 + 3 + 2 = 7

∴ Number of ways of drawing 2 balls out of 7 = 7C2 = (7 × 6) / (2 × 1) = 42/2 = 21

Number of balls other than blue = 5

∴ Number of ways of drawing 2 balls out of 5 = 5C2 = (5 × 4) / (2 × 1) = 20/2 = 10

∴ Required Probability = 10/21

Explanation

Let's calculate the population after 2 years:

Year 1:

Population = 50,000 + (4% of 50,000)

= 50,000 + 0.04 * 50,000

= 50,000 + 2,000

= 52,000

Year 2:

Population = 52,000 + (4% of 52,000)

= 52,000 + 0.04 * 52,000

= 52,000 + 2,080

= 54,080

The population after 2 years will be 54,080.

Explanation

Let the height of the building be x meters.

Less lengthy shadow, Less in the height (Direct Proportion)

∴ 40.25 : 28.75 :: 17.5 : x ⇔ 40.25 × x = 28.75 × 17.5

Explanation

25% of x = 150

0.25x = 150

x = 150 / 0.25

x = 600

Explanation

Let's solve:

3 men = 6 boys (given)

1 man = 2 boys

Work done by 3 men or 6 boys in 20 days:

Let's calculate work done by 1 boy in 1 day:

6 boys * 20 days = 120 boy-days

Now, 6 men and 8 boys:

6 men = 6 * 2 = 12 boys

Total = 12 boys + 8 boys = 20 boys

Time taken = 120 boy-days / 20 boys = 6 days

Explanation

15 men complete the work in 8 days

Total work = 15 men * 8 days = 120 man-days

Now, to complete the work in 10 days:

120 man-days / 10 days = 12 men

Explanation

1/240 * n * 4 = 6 becomes:

1/240 * 360 * 4 = 6

we simplify to get:

6 = 6 confirming that our calculation of the number of people required is good.

the answer is that it would require 360 men to fill 6 holes in 4 months.