Data Interpretation Discussion

**Common Information**

Answer the questions on the basis of the information given below.

There are only four companies’ viz. P, Q, R and S that manufacture shirts in the market. The shirts manufactured by these companies are made of one or the other of the five types of cloth viz. Silk, Cotton, Linen, Khadi and Polyester.

The following pie-charts provide information about the number of shirts of each of the types of cloth manufactured by the company as a percentage of the total number of shirts manufactured by that company.

The following chart provides information about the number of Linen shirts manufactured by each of the companies as a percentage of the total number of Linen shirts manufactured by all the companies.

Q. |
Each of the two companies Q and S sell each shirt manufactured by them at Rs.10 above their cost price. If the difference between the profit generated by both the companies is Rs.15000, then what is the difference between the number of Polyester shirts manufactured by the companies P and R? (Assume that all the shirts that are manufactured are sold). |

✔ A. |
4800 |

✖ B. |
1500 |

✖ C. |
3000 |

✖ D. |
Cannot be determined |

**Solution:**

Option(**A**) is correct

Let the total number of Linen shirts manufactured by all the given companies $= X$

Therefore, the number of Linen shirts manufactured by the companies P, Q, R and S is:

$\dfrac{X}{4}, \dfrac{X}{4}, \dfrac{X}{5}$ and $\dfrac{3X}{10}$ respectively.

Therefore, the total number of shirts manufactured by the companies P, Q, R and S is:

$\dfrac{5X}{6}, \dfrac{5X}{4}, \dfrac{4X}{3}$ and $\dfrac{6X}{5}$ respectively.

Given that the difference between the profit generated by both the companies is Rs.15000.

From the explanation given above, the number of shirts

manufactured by the companies Q and S is:

$\dfrac{5X}{4}$ and $\dfrac{6X}{4}$ respectively.

Difference in the profit generated by the two companies Q and S will give:

$=\dfrac{5X}{4} - \dfrac{6X}{5} = \dfrac{X}{20} = \dfrac{15000}{10} =1500$

$⇒ X = 3 × 10^4$

Difference between the number of Polyester shirts manufactured by the companies P and R is:

$=\left(\dfrac{22}{100}×\dfrac{4X}{3}\right)- \left(\dfrac{16}{100}×\dfrac{5X}{6}\right)$

$=\dfrac{4X}{25}$

$=\dfrac{(4×3×10^4)}{25}$

$= \textbf{4800}$

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The way you are going ahead with the question, sure you won't get the value of $X$.

I have a doubt.

let's say the cost price of each shirt is $C$ and they are sold at Rs. 10 above their cost price. this means they are sold at Rs. $(C+10)$.

and we have $\dfrac{X}{20}$ shirts left => $(C+10) \times \dfrac{X}{20} = 15000$

which we can't find the value of $X$ unless we have $C$.

Please correct me if I am wrong.

Thanks