Question

33. A fort had provisions for 1200 men for
20 days. If 400 men joined the fort on
the first day, how long would the food
last at the same rate?
UNV 1997]​

Answer 1

Answer:

The food would last for 60 days for 400 men.

Step-by-step explanation:

The food would last for 60 days for 400 men.

• Given,

Food for 1200 men lasts for 20 days, means 1200 men is proportional to 20 days. Then, 1200 : 20

• In the question, the number of days for which food would last at the same rate for 400 men, has been asked.

• Now, if the number of men decreases, the number of days for which the food lasts should increase.

• Let x be the number of days for which the food lasts for 400 men. Then 400 : x

• The quantity of food remains same in both the cases. Therefore,

  1200 : 20 :: 400 : x

=> 1200/400 = x/20

=> x = (1200 × 20) / 400

=> x = 60

Therefore, the food would last for 60 days for 400 men.

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