Question

Question No. 1 of 10 | 1 Marks
80 villagers repaired 2/3rd of a broken bank of river in 6 hours. More
villagers join the work and complete the work in next 2 hours working at the
same rate. The numbers of new villagers involved are:​

Answer 1

Answer: 40 villagers

Step-by-step explanation:

Given:

80 villagers repair $\dfrac{2}{3} rd$ of broken bank of river in 6 hours

To find : Number of villagers that should join the work to complete the $\dfrac{1}{3} rd$ of broken bank in 2 hours

Let $M_1 = 80$,  $T_1 = 6 hours$,  $W_1 = \dfrac{2}{3}$

and $M_2 = x$, $T_2 = 2 hours$, $W_2 =\dfrac{1}{3}$

Now as we know

$\dfrac{M_1\times T_1 }{W_1} =\dfrac{M_2\times T_2 }{W_2}\\\\\Rightarrow \dfrac{80\times 6}{\dfrac{2}{3} } =\dfrac{x\times2}{\dfrac{1}{3}}\\\\\\\Rightarrow x=120$

Number of villagers should join to complete the work in 2 hours = 120- 80 = 40

Hence,  Number of villagers should join to complete the work in 2 hours is 40

Answer 2

Answer:

The numbers of new villagers involved are 40 .

Step-by-step explanation:

no. villagers (n)             time (t)                  work(w)

         80                              6                            2/3

      (80+x)                            2                            1/3

Where , x = numbers of new villagers involved .

n & t are inversly proportional .

n & w are directly proportional .

n = k * (w/t)  [ k = constant ] .

or, 80 = k * (2/3)/6.

or , k = 80 * 6 * (3/2).

or , k = 720.

(80+x) = 720 * 1/3 * 1/2 .

or , 80+x = 120 .

or , x = 40 .

So , The numbers of new villagers involved are 40 .

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