Question

A garrison of 900 men had provisions for 42 days. However a reinforcement of 500 men arrived. For how many days will the food last now?

Answer 1

Solution :-

Let the required number of days be x

More men less days - It is an inverse variation.

⇒ 1400 : 900 : : 42 : x

⇒ 1400x = 900*42

⇒ x = 37800/1400

⇒ = 27 days

So, the food will last for 27 days, when a reinforcement of 500 men arrived.

Answer.

Answer 2

Given:

900 men has food provisions for 42 days.

Let number of men [ x ] = 900(x1) , 1400(x2) (500 more men arrived)

number of days [ y ] = 42(y1) , y2

If there are more men, food provisions for them will be there for less days.

So, it is case of an inverse proportion.

x1y1 = x2y2

900 × 42 = 1400 × y2

y2 = 900 ×42 / 1400

y2= 9 × 42 / 14

y2= 9 ×3

y2= 27 days

Hence, the food will last for 27 days, when a reinforcement of 500 men arrived.

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