Question

A firm needs both skilled labour and unskilled labour. Skilled wage = ₹ 40{,000 per month; unskilled wage = ₹ 15{,}000 per month. The total wage bill for 100 labourers is ₹ 23{,}75{,}000 in a month. How many skilled labour are employed? (in Integer)}

Hint:

In mixture/wage problems, set one variable for one group, express the other as the complement (here \(100-x\)), and form a single linear cost equation to solve quickly.

Answer 1

Step 1: Define variables.
Let the number of skilled workers be \(x\). Then unskilled workers \(=100-x\).

Step 2: Set up wage equation.
\[ 40{,}000\,x + 15{,}000\,(100-x) \;=\; 23{,}75{,}000 \]

Step 3: Simplify and solve.
\[ 40{,}000x + 15{,}00{,}000 - 15{,}000x = 23{,}75{,}000 \Rightarrow 25{,}000x = 8{,}75{,}000 \] \[ x = \frac{8{,}75{,}000}{25{,}000} = 35 \] \[ \boxed{\text{Skilled labour employed} = 35} \]