Question

2 men and 3 boys can do piece of work in 14 days , while 4 men and 5 boys can do it in 8 days . How long would it take 1 boy to finish the work ? ​

Answer 1

✴OLA!!✴

⤵⤵ANSWER⤵⤵

Let 1 man can finish the work in x days and 1 boy can finish it in y days . then

1 man's 1 day work = 1/x and 1 boy's one day work = 1/y

given 2 men and 3 boys can do the work in 14 days

therefore , 2 men's one day work + 3 boys one day work = 1/14

=> (2/x ) + (3/y) = 1/14...............................(1)

Also 4 men and 5 boys can finish the work in 8 days .

therefore , 4 men's one day work + 5 boys one day work = 1/8

=>( 4/x ) + (5/y) = 1/8 ...........................(2)

multiply (1) by 2,( 2) by 1 , we have :

4/x + 6/y = 1/7

4/x + 5/y = 1/8

-......-.........-.....................(subtracting)

1/y = (1/7)-(1/8)= 8-7/7×8 = 1/56

therefore , y = 56

hence , one boy can finish the work in 56 days .✔✔

Hope it helps u✌

tysm❤

Answer 2

• Let men = x and boy = y.

» 2 men and 3 boys can do piece of work in 14 days.

A.T.Q.

=> $\dfrac{2}{x}$ + $\dfrac{3}{y}$ = $\dfrac{1}{14}$

• Let $\dfrac{1}{x}$ = a and $\dfrac{1}{y}$ = b

=> 2a + 3b = $\dfrac{1}{14}$

=> 14(2a + 3b) = 1

=> 28a + 42b = 1 ________ (eq 1)

» 4 men and 5 boys can do it in 8 days.

A.T.Q.

=> $\dfrac{4}{x}$ + $\dfrac{5}{y}$ = $\dfrac{1}{8}$

=> 4a + 5b = $\dfrac{1}{8}$

=> 8(4a + 5b) = 1

=> 32a + 40b = 1 _________ (eq 2)

Multiply (eq 1) with 40 and (eq 2) with 42 then we get..

=> 1120a + 1680b = 42 ______ (eq 3)

=> 1344a + 1680b = 40 ______ (eq 4)

On solving (eq 3) and (eq 4) by elimination method .. we get;

=> a = $\dfrac{1}{112}$

Put value of a in (eq 1)

=> $\dfrac{28}{112}$ + 42b = 1

=> 28 + 4704b = 112

=> 4704b = 84

=> b = $\dfrac{1}{56}$

Now ..

→ y = $\dfrac{1}{b}\:=\:\dfrac{1}{\frac{1}{56}}$

→ y = 56

_____________________________

One boy take 56 days to complete the work.

________ [ ANSWER ]

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