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# 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?  Answer Verified
Hint: First take the price of the shirt as ‘s’. 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.

Complete step-by-step answer:
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, let’s take the price of the shirt as ‘s’.

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 ‘s’ 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.

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