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. |
Common Information Question: 2/5 What is the minimum possible number of shirts that should have been manufactured by all the companies combined such that for each company, the number of shirts of each of the types of cloth manufactured by it is an integer? |
✖ A. | 6,925 |
✖ B. | 5,540 |
✔ C. | 27,700 |
✖ D. | Cannot be determined |
Solution:
Option(C) 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.
Assume that the total number of Linen shirts manufactured by all the companies is 100.
Therefore, the total number of Linen shirts manufactured by the companies P, Q, R and S is 25, 25, 20 and 30 respectively.
The following table lists down the number of shirts of each type of cloth manufactured by each of the companies, when the total number of Linen shirts manufactured is 100.
Table below can be scrolled horizontally
Company | Silk | Cotton | Linen | Khadi | Polyester | Total |
---|---|---|---|---|---|---|
P |
15 |
20 |
25 |
10 |
13.33 |
83.33 |
Q |
37.5 |
25 |
25 |
18.75 |
18.75 |
125 |
R |
40 |
28 |
20 |
16 |
29.33 |
133.33 |
S |
22.8 |
19.2 |
30 |
24 |
24 |
120 |
Therefore, for the number of shirts of each type of cloth to be an integer we need to convert all the fractional values in the table to integers.
In order to do so, we need to multiply the entries for P with 3, the entries for Q with 4, the entries for R with 3 and the entries for S with 5. So, if we multiply all the entries with the l.c.m of 3, 4, 3 and 5, that will do the needful.
Minimum possible number of shirts manufactured by all the companies:
$= (83.33 + 125 + 133.33 + 120) × (3 × 4 × 5)$
$= \textbf{27,700}$