Question

Selling price of a shirt and a coat is Rs.4000. The cost price of a shirt is 58.33% of the cost price of a coat and so amount of profit on both the shirt and coat is same, then the price of the shirt could be:
A) 2100
B) 2120
C) 2552
D) 1120

Answer 1

Hint: To solve this question first we will derive the ratio of cost price both in whole numbers. From given data and assuming cost price and profit as variables we will obtain a linear equation in two variables. Using a hit and trial method we will solve the linear equation to get the answer.

Complete step-by-step answer:
According to the question,
The cost price of a shirt is 58.33% of the cost price of a coat.
Let if the cost price of the coat is 100, then the cost price of the shirt will be 58.33.
Hence the ratio of cost price of shirt and the coat \[ = \dfrac{{58.33}}{{100}}\]
Converting the above into a smaller fraction we get the ratio of cost price of shirt and the coat \[ = \dfrac{{7.29}}{{12.5}}\]
Converting it into its nearby whole number we get the ratio of cost price of shirt and the coat \[ = \dfrac{7}{{12}}\]
So, let the cost price of the shirt be 7x
And the cost price of coat be 12x
Again it is given in the question that profit on both the shirt and coat is the same.
Let the profit on each be y and the total profit be 2y
We know that the selling price = cost price + profit
Hence, the selling price of shirt is $ 7x + y $
And the selling price of the coat is $ 12x + y $
It is given in the question that selling price of a shirt and a coat is Rs.4000
 $ \therefore $ $ 7x + y + 12x + y = 4000 $
 $ \Rightarrow 19x + 2y = 4000 $ …………………. (1)
As we have only one equation of two variables we have to solve it using a hit and trial method.
We know that the value of x can’t be less than zero because the price can’t be negative.
So, for y = 0,
Putting it in equation 1 we get,
 $ 19x + 2 \times 0 = 4000 $
 $ \Rightarrow 19x = 4000 $
 $ \Rightarrow x = \dfrac{{4000}}{{19}} = 210.5 $
Hence the selling price of shirt, $ 7x = 7 \times 210.5 = 1473.5 $
For minimum value of y, price of shirt is Rs.1473.5 i.e. maximum price of shirt can be Rs.1473.5
Price of the shirt can’t be more than Rs.1473.5. it is either Rs.1473.5 or less than this.
If we see the options, there is no option of 1473.5 And there is only one option which is less than 1473.5 is 1120(option D)
Hence option D is the correct answer.

The price of the shirt could be Rs.1120.

Note: We can’t take the value of y as negative integers because price can’t be negative.
You might be confused as to why we did not extend the method to get the actual value. But as we have options and we concluded that price can’t be more than Rs.1473.5.
Moreover, it is asked in the question that ‘the price of the shirt could be’ i.e. we may not get the actual answer.
Hit and trial method is made to balance the equation by using the smallest whole number coefficient.
If options are not given, you can extend the method to get an actual or approximate answer.
You should practice more such questions.