For 50 students, food is sufficient for 45 days
∴ For 1 student, food is sufficient for 45 x 50 days

Correct Option: C

For 50 students, food is sufficient for 45 days
∴ For 1 student, food is sufficient for 45 x 50 days
and for 75 students, food is sufficient for (45 x 50)/75 days. i,e., for 30 days.

3 men ≡ 6 boys
⇒ 1 man ≡ 2 boys
∴ 4 men + 4 boys ≡ 4 men + 2 men = 6 men
∵ 3 men can do a work in 18 days.
∴ 1 man can do a work in 18 x 3 days.

Correct Option: D

3 men ≡ 6 boys
⇒ 1 man ≡ 2 boys
∴ 4 men + 4 boys ≡ 4 men + 2 men = 6 men
∵ 3 men can do a work in 18 days.
∴ 1 man can do a work in 18 x 3 days.
∴ Required number of days = (18 x 3)/6 = 9 days

Let the required number of days be N.
More men, Less days (indirect proportions)

Correct Option: A

Let the required number of days be N.
More men, Less days (indirect proportions)
Soldiers 90 : 72
Ratio 9 : 10
N = (72 x 54 x 10)/(90 x 9) = 48 days

∵ For 50 students, food is sufficient for 45 days.
∴ For 1 students, food is sufficient for 45 x 50 days.

Correct Option: C

∵ For 50 students, food is sufficient for 45 days.
∴ For 1 students, food is sufficient for 45 x 50 days.
∴ For 75 students, food is sufficient for (45 x 50)/75 days i.e., for 30 days .

Let the number of soldiers transferred be N
Now, the food would last for 25 days for (2000 - N) soldiers.
Less men, More days (indirect proportion)
25 : 20 : : 2000 : (2000 - N)

Correct Option: A

Let the number of soldiers transferred be N
Now, the food would last for 25 days for (2000 - N) soldiers.
Less men, More days (indirect proportion)
25 : 20 : : 2000 : (2000 - N)
⇒ 2000 - N = (2000 x 20)/25
⇒ 2000 - N = 1600
∴ N = 2000 - 1600 = 400