Question

15 men, 18 women and 12 boys working together earned Rs 2070. If the daily wages of a man, a woman and a boy are in the ratio 4:3:2 then, what is the daily wages (in Rs) of 1 man, 2 women and 3 boys?
$
  {\text{A}}{\text{. 135}} \\
  {\text{B}}{\text{. 180}} \\
  {\text{C}}{\text{. 240}} \\
  {\text{D}}{\text{. 205}} \\
 $

Answer 1

Hint: Here, we will proceed by letting the daily wages of a man, a woman and a boy according to the ratio given in the problem and then we will obtain an equation in one variable and then solve for that variable.

Complete step-by-step answer:

Given, Total earnings of 15 men, 18 women and 12 boys = Rs 2070

Also given, Daily wages of a man : Daily wages of a woman : Daily wages of a boy = 4:3:2

So, we can let that the daily wages of a man, a woman and a boy be 4k, 3k and 2k

respectively

i.e., Daily wages of a man = 4k

$ \Rightarrow $Daily wages of 15 men = $15\left( {4k} \right) = 60k$

Daily wages of a woman = 3k

$ \Rightarrow $Daily wages of 18 women = $18\left( {3k} \right) = 54k$

Daily wages of a boy = 2k

$ \Rightarrow $Daily wages of 12 boys = $12\left( {2k} \right) = 24k$

As, Total earnings of 15 men, 18 women and 12 boys = Daily wages of 15 men + Daily wages of 18 women + Daily wages of 12 boys

By substituting the values in the above equation, we get

$

   \Rightarrow 2070 = 60k + 54k + 24k \\

   \Rightarrow 138k = 2070 \\

   \Rightarrow k = \dfrac{{2070}}{{138}} \\

   \Rightarrow k = 15 \\

 $

Daily wages of a man = 4k = $4\left( {15} \right)$ = Rs 60

Daily wages of a woman = 3k = $3\left( {15} \right)$ = Rs 45

Daily wages of a boy = 2k = $2\left( {15} \right)$ = Rs 30

Daily wages of 1 man, 2 women and 3 boys = Daily wages of a man + 2(Daily wages of a woman) + 3(Daily wages of a boy)

$ \Rightarrow $Daily wages of 1 man, 2 women and 3 boys = 60 + 2(45) + 3(30) = 60 + 90 + 90 = Rs 240

Therefore, the daily wages of 1 man, 2 women and 3 boys is Rs 240.

Hence, option C is correct.

Note: In this particular problem, if we take the given ratio separately we will get to know why exactly we are letting the daily wages of a man, a woman and a boy as 4k, 3k and 2k respectively. Since, $\dfrac{{{\text{Daily wages of a man}}}}{{{\text{Daily wages of a woman}}}} = \dfrac{4}{3} = \dfrac{{4k}}{{3k}}$, $\dfrac{{{\text{Daily wages of a woman}}}}{{{\text{Daily wages of a boy}}}} = \dfrac{3}{2} = \dfrac{{3k}}{{2k}}$ and $\dfrac{{{\text{Daily wages of a man}}}}{{{\text{Daily wages of a boy}}}} = \dfrac{4}{2} = \dfrac{{4k}}{{2k}}$.