An army regiment has provisions for 400 soldiers for 80 days. After 10 days, 50 soldiers moved out of the regiment. How long would the food last at the same rate?
Answers
80 days would food last at the same rate.
An army regiment has provision for 400 soldiers for 80 days.
let one unit of food is for 400 soldiers for 80 days.
then, 1/8 unit of food is for consume in 10 days by 400 soldiers.
remaining = 1 - 1/8 = 7/8 th part of food.
now, 7/8 th part of food is for (400 - 50) soldiers for x days (let).
using formula,
M1D1/W1 = M2D2/W2
here, M , D and W represent number of soldiers, number of days and food content respectively.
M1 = 400, D1 = 80 , W1 = 1, M2 = 350 , D2 = x and W2 = (7/8)
⇒400 × 80/1 = 350 × x/(7/8)
⇒400 × 80 × 7/8 = 350x
⇒x = (400 × 80 × 7)/(350 × 8)
= 80 days
hence, 80 days would food last at the same rate.
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