Certainly! Let's break down the solution step by step.
We have three labours whose wages are distributed in the ratio [tex]\( 2:3:5 \)[/tex]. The total wage given is Rs. 66,000. We need to find out the wage of each labour.
### Step 1: Understand the Ratio
The given ratio is [tex]\( 2:3:5 \)[/tex]. This tells us how the total wage is divided among the three labours.
### Step 2: Calculate the Sum of the Ratio Parts
Add the parts of the ratio together to understand how many total parts we are dealing with:
[tex]\[ 2 + 3 + 5 = 10 \][/tex]
So, the total ratio parts sum to 10.
### Step 3: Determine the Wage for Each Labour
Next, we need to calculate each labour's wage based on their ratio part of the total wage.
- Labour 1:
- The ratio part for Labour 1 is 2.
- The total number of ratio parts is 10.
- The wage for Labour 1 is calculated as:
[tex]\[
\text{Labour 1's wage} = \left(\frac{2}{10}\right) \times 66000 = 13200
\][/tex]
- Labour 2:
- The ratio part for Labour 2 is 3.
- The wage for Labour 2 is calculated as:
[tex]\[
\text{Labour 2's wage} = \left(\frac{3}{10}\right) \times 66000 = 19800
\][/tex]
- Labour 3:
- The ratio part for Labour 3 is 5.
- The wage for Labour 3 is calculated as:
[tex]\[
\text{Labour 3's wage} = \left(\frac{5}{10}\right) \times 66000 = 33000
\][/tex]
### Step 4: Verify the Solution
To ensure our calculations are correct, we can add the individual wages and check if they sum to the total wage:
[tex]\[
13200 + 19800 + 33000 = 66000
\][/tex]
Thus, the wages for each labour, correctly distributed according to the ratio 2:3:5, are:
- Labour 1: Rs. 13,200
- Labour 2: Rs. 19,800
- Labour 3: Rs. 33,000
