Question

An army camp of 120 soldiers has rations for 50 days , if 40 soldiers join them after 10 days , how long will the rations last​

Answer 1

Step-by-step explanation:

Number of troops to begin with 120. total rations available for 50 days.After 10days., 30% of the rations would have been consumed.120 troops would consume the remaining rations (75%) in 15 days.Adding 40 additional troops, the number would increase to 160 and that means rations would be consumed faster.

120 troops = 50 days

160 troops = ? days

Since the number of days are inversely proportional to the number of troops., we can compute the number of days the pending rations (d) would last as

d=120*50/160 or d=25 days

d = 40 * 15/50 or d = 12 days.

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Answer 2

Answer:-

$30 \: \: days$

Step - by - Explanation:-

¤ At the end of 10 days the camp has enough ration to provide for 120 for (50 - 10)days = 40 days. Since the number of soldiers increases, the ration will last for less days than planned. In other words, an increase in the number of soldiers will mean a decrease in the number of days. Hence, this is a case of inverse proportion.

• Thus, ratio of the number of soldiers =

$\frac{1}{ratio \: of \: the \: numbers \: of \: days}$

• Therefore,

$\frac{120}{120 + 40} = \frac{1}{ \frac{40}{x} }$

where x is the number of days for which the ration will last.

• Therefore,

$\frac{120}{160} = \frac{x}{40} \: \: or \: \: x \: = \: \frac{120}{160} \times 40 \\x = \frac{3}{4} \times 40 = 30 \: days \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

•$here \: \frac{3}{4} \: \: is \: \: the \: \: multiplying \: \: \\ ratio. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hope this answer will help u⭐⭐⭐⭐⭐