Question

1200 men can finish a stock of food in 35 days. How many more men should join them so that the food may last for 25 day

Answer 1

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Let the number of men joined be ‘x’ men

Total men = 1200 Men 1200 x Time (days) 35

25 We know k = xy 1200 × 35 = x × 25 x = (1200×35)/25 = 1680

So, 1680 – 1200 = 480 Men

∴ 480 men should join for the same stock to last for 25 days.

Answer 2

Given:

1200 men can finish a stock of food in 35 days.

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To find:

Number of men that should join the existing ones to finish the stock of food in 25 days.

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Solution:

$\boxed {\sf {\large {Understanding\ the\ question}}}$

Here the concept of inverse proportion is used where one quantity increases while the other quantity decreases.

In the given question, we are provided with two quantities, number of men and number of days. As the number of days decreases, then its obvious that number of men will increase to finish the same stock of food in less number of days. Therefore it is in inverse proportion. (Refer to the attachment for the table)

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We know that,

$\sf {x_{1} y_{1} = x_{2} y_{2}}$ [Here x is number of men and y represents number of days]

On substituting the values,

$\sf {1200 \times 35 = 25x_{2}}$

$\sf {4200 = 25x_{2}}$

$\sf \dfrac {4200}{25} = x_{2}$

$\boxed {\bf {\red {1,680 = x_{2}}}}$

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Now,

(1,680 - 1,200) men

= 480 men

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Final answer:

480 more men will be needed to finish the same stock of food in 25 days.