Question

The work done by a man , a woman and a child are in the ratio 3 : 2 : 1. If the daily wages of 20 men , 30 women and 36 children amount to Rs . 78 , what will be the wages of 15 men , 21 women and 30 children for 18 weeks?
a.Rs.7371
b.Rs.8645
c.Rs.9000
d.Rs.9500

Answer 1

Hint: We are given the ratio with which we get the work done by the man, woman and children is 3a , 2a , a and equating we obtain than a man does thrice the work of a child and a woman does twice the work of the child . substituting this in the given data we get the amount paid for a child per day. With this we can calculate the amount paid for 15 men , 21 women and 30 children for 18 weeks

Complete step-by-step answer:
We are given the ratio of work done by man , women and children is 3 : 2 : 1
Whenever we are given a ratio we can assume that the amount of work done by man , woman and children is 3a , 2a , a respectively , where a is any positive number
Lets represent man by M and woman by W and children by C
Now we get that the work done by them to be
$
   \Rightarrow M = 3a \\
   \Rightarrow W = 2a \\
   \Rightarrow C = a \\
$
From the last equation we get that
$
   \Rightarrow M = 3C \\
   \Rightarrow W = 2C \\
$
Let this be equation (1)
Now we are given that the daily wages of 20 men , 30 women and 36 children is Rs.78
So ,
$ \Rightarrow 20M + 30W + 36C$
Using equation (1) we get
$
   \Rightarrow 20(3C) + 30(2C) + 36C \\
   \Rightarrow 60C + 60C + 36C \\
   \Rightarrow 156C \\
$
Now from this we get 156 children get Rs. 78
So now to calculate the amount one child gets we can divide 78 by 156
$
   \Rightarrow 156C = 78 \\
   \Rightarrow C = \dfrac{{78}}{{156}} = \dfrac{1}{2} \\
$
Now this tells that each child gets Rs.$\dfrac{1}{2}$per day
Now we need to find the wages of 15 men , 21 women and 30 children for 18 weeks
So,
$ \Rightarrow 15M + 21W + 30C$
Using equation (1) we get
 $
   \Rightarrow 15(3C) + 21(2C) + 30C \\
   \Rightarrow 45C + 42C + 30C \\
   \Rightarrow 117C \\
$
So now we need to calculate the wages of 117 children for 18 weeks
We have that the wages for one child per day is Rs. $\dfrac{1}{2}$
The wages for 117 children per day is
$ \Rightarrow \dfrac{1}{2}*117 = 58.5$
Now the number of days in 18 weeks is 18 * 7 =126
Therefore the total wages for 18 weeks is
$ \Rightarrow 58.5*126 = Rs.7371$
Therefore the correct option is a.

Note: Whenever we are dealing with problems related to ratio many students tend to take the work done by the man , woman and child to be 3 , 2 , 1. But it is a mistake they are 3a,2a and a where a is a positive integer