Question

12 men or 15 women can finish a work in 10 days . How many days will 7 men and 10 women take to finish the same work together ?​

Answer 1

Answer:

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Step-by-step explanation:

= 12 men and 15 women = 10 days

= 7 men and 10 women = ?

= 12 + 15 = 27 persons ( x1 ) = 10 days ( y1 )

= 7 + 10. = 17 persons ( x2 ) = ? ( y2 )

= x1 = y1

x2 y2

= 27 = 10

17. y2

= y2 = 10 × 17

27

= y2 = 6.29 days

Answer 2

Answer:

8

Step-by-step explanation:

Given,

12 men (or) 15 women can finish a work in 10 days

To Find :-

How many days will 7 men and 10 women take to finish the same work?

Solution :-

As, 12 men can finish a work in 10 days :-

$\implies$One day work of 12 men = 1/10days

One day work of 1 men = $\dfrac{1}{10}\times \dfrac{1}{12}$

= $\sf\dfrac{1}{120}$

As, 15 women can finish a work in 10 days

$\implies$One day work of 15 women = 1/10days

One day work of 1 women = $\dfrac{1}{10}\times \dfrac{1}{15}$

= $\sf\dfrac{1}{150}$

As we need to find, In How many days will 7 men and 10 women take to finish the same work together:-

Since, work of 7 men = $\sf 7\times\dfrac{1}{120}$

= $\sf\dfrac{7}{120}$

Work of 10 women = $\sf 10\times \dfrac{1}{150}$

= $\sf\dfrac{10}{150}$

As we need to find work done by 7 men and 10 women together we need to add both the values :-

One day work done by 7 men and 10 women together :-

$= \dfrac{7}{120}+\dfrac{10}{150}$

L.C.M of 120,150 = 600

$= \bigg(\dfrac{7}{120}\times\dfrac{5}{5}\bigg) + \bigg(\dfrac{10}{150}\times\dfrac{4}{4}\bigg)$

$= \dfrac{35}{600}+\dfrac{40}{600}$

$= \dfrac{35+40}{600}$

$= \dfrac{75}{600}$

$= \dfrac{1}{8}$

As it was only one day work of them together, But we need Total work of them together. So we do reciprocal it.

$= \dfrac{1}{\dfrac{1}{8}}$

= 8

Since, Number of days it taken to 7 men and 10 women to work together to finish the work is "8 days".