direct and inverse varistion
A garrison of 120 men has provision for 30 days. At the end of five days five more men joined them. How many days can they sustain on the remaining provision.
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Answer:Given that,
Number of men = 120
Time = 30 days
At the end of 5 days, 5 more men joined them.
For 120 men there is provision for 30 days
If 1 man needs 1 unit of provision in a day
Then, total provision =
Total provision =3600
120 men in 5 days will take =
120 men in 5 days will take = 600 unit of provision
Remaining provision = 3600-600
Remaining provision =3000 units
5 more men joined and now there are total 125 men
We need to calculate the days on the remaining provision
1 day provision requirement for 125 men = 125 units
Days for which they can sustain on remaining provision =
Days for which they can sustain on remaining provision =24 days
Hence, They can sustain on remaining provision for 24 days.
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Let after the joining of 5 men (after 5 days), It took x days to sustain on the remaining provision then,
According to the question-
120×30=120×5+125×x
(120×30)−(120×5)=125x
120(30−5)=125x
120×25=125x
120=5x
x=24 days
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