Question

# 12 days payment to the servant in a cloth showroom in festival season is Rs. 400 plus one shirt. The servant leaves after 9 days and receives Rs. 280 and a shirt. What is the price of the shirt?

Hint: First take the price of the shirt as â€˜sâ€™. The total payment should be received (400 + s) if he worked for 12 days. But he worked for 9 days he will receive $\dfrac{9}{12}\left( 400+s \right)$ but in the question, it is already said that he received (280 + s). So just equate the two expressions to find the value of the shirt.

In the question, a servant was promised a sum of Rs. 400 and a shirt. If he serves in the cloth showroom in the festive season for 12 days. But the servant leaves after 9 days and receives Rs. 280 and a shirt, then we have to find the value of the shirt.

See as the servant works on a daily basis then we should apply the unitary method to solve this equation.

First, letâ€™s take the price of the shirt as â€˜sâ€™.

So the total payment the servant would have got in 12 days would be Rs. (400 + s).

So we can say,

In 12 days of work, a servant would get a sum of (400 + s).

Now in 1 day of work a servant would get Rs. $\left( \dfrac{400+s}{12} \right)$.

But as a servant worked for only 9 days, he will get Rs. $9\times \dfrac{\left( 400+s \right)}{12}$.

But in the question, it is said that the servant got a payment of Rs. (240 + s).

So now we can say that,

$\dfrac{9}{12}\left( 400+s \right)=\left( 280+s \right)............\left( i \right)$

Where â€˜sâ€™ is the price of a shirt.

After cross multiplication in equation (i) we can write it as,

$9\left( 400+s \right)=12\left( 280+s \right)$
Now on further multiplication we get,

$3600+9s=3360+12s.............\left( ii \right)$

Now subtracting 3360 on both the sides of the equation (ii) we get,
\begin{align} & 3600-3360+9s=12s \\ & \Rightarrow 240+9s=12s...................\left( iii \right) \\ \end{align}

Now subtracting 9s from both the sides of the equation (iii) we get,
\begin{align} & 12-9s=240 \\ & \Rightarrow 3s=240 \\ & So,\ s=\dfrac{240}{3}=80 \\ \end{align}

Hence, the price of a shirt which the servant got is Rs. 80.

Note: Students get confused about why 12 is divided and why 9 is multiplied to (400 + s). Actually for this problem rule follows that if a person works for more number of days he will get more money than that person who comparatively worked for less number of days.