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Four friends Robert, Thomas, Jack, and Mary works in the same factory and if their salary is as follows: Salary of Robert is 10% less than Thomas and Thomas gets 25% less than Jack and Jack gets 20% less than Mary and the salary of Robert is Rs. 3600, then find the salary receive by Mary.
(A) Rs. 3500
(B) Rs. 4000
(C) Rs. 4500
(D) Rs. 4800
(E) None of these

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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Hint: Assume that the salary of Thomas is Rs. x. Robert’s salary is 10% less than that of Thomas. So, the salary of Robert = Rs. (x-10% of x). But the salary of Robert is Rs. 3600. Now, compare and get the value of x. Similarly, assume that the salary of Jack is Rs. y. Thomas’s salary is 25% less than that of Jack so, the salary of Thomas = Rs. (y-25% of y). But earlier we calculated the salary of Thomas. Now, compare and get the value of y. Again, assume that the salary of Mary is Rs. z. The salary of Jack is 20% less than that of Mary so, the salary of Jack is Rs. (z-20% of z). At last, solve it further and get the value of z.

Complete step-by-step solution
According to the question, we are given that there are four friends Robert, Thomas, Jack, and Mary work in the same factory. Also, the Salary of Robert is 10% less than Thomas and Thomas gets 25% less than Jack and Jack gets 20% less than Mary and the salary of Robert is Rs. 3600.
First of all, let us assume that the salary of Thomas is Rs. x …………………………………………(1)
Since Robert’s salary is 10% less than that of Thomas so,
The salary of Robert = Rs. (x-10% of x) = Rs. \[x-\dfrac{10x}{100}=\dfrac{90x}{100}=\dfrac{9x}{10}\] ………………………………………………(2)
But we are given the salary of Thomas which is equal to Rs. 3600 ……………………………(3)
On comparing equation (2) and equation (3), we get
\[\begin{align}
  & \Rightarrow \dfrac{9x}{10}=3600 \\
 & \Rightarrow x=\dfrac{3600\times 10}{9} \\
 & \Rightarrow x=400\times 10 \\
\end{align}\]
\[\Rightarrow x=4000\]
So, the salary of Thomas is Rs. 4000 ……………………………………..(4)
Similarly, let us assume that the salary of Jack is Rs. y …………………………………………………..(5)
Since, Thomas’s salary is 25% less than that of Jack so,
The salary of Thomas = Rs. (y-25% of y) = \[y-\dfrac{25y}{100}=\dfrac{75y}{100}=\dfrac{3y}{4}\] ………………………………………………..(6)
But, from equation (4), we also have the salary of Thomas.
Now, on comparing equation (4) and equation (6), we get
\[\begin{align}
  & \Rightarrow 4000=\dfrac{3y}{4} \\
 & \Rightarrow y=\dfrac{4000\times 4}{3} \\
\end{align}\]
\[\Rightarrow y=\dfrac{16000}{3}\]
So, the salary of Jack is Rs. \[\dfrac{16000}{3}\] ……………………………………..(7)
Similarly, let us assume that the salary of Mary is Rs. z …………………………………………………..(8)
Since Jack’s salary is 20% less than that of Mary so,
The salary of Jack = Rs. (z-20% of z) = \[z-\dfrac{20z}{100}=\dfrac{80z}{100}=\dfrac{4z}{5}\] ………………………………………………..(9)
But, from equation (7), we also have the salary of Jack.
Now, on comparing equation (7) and equation (9), we get
\[\begin{align}
  & \Rightarrow \dfrac{16000}{3}=\dfrac{4z}{5} \\
 & \Rightarrow z=\dfrac{16000\times 5}{3\times 4} \\
 & \Rightarrow z=\dfrac{20000}{3} \\
\end{align}\]
Therefore, the salary of Mary is Rs. \[\dfrac{20000}{3}\]. Hence, the correct option is (E).

Note: Whenever this type of question appears, where the salary of one person is given in terms of the salary of another person. Always approach this type of question by assuming the salary of one person in terms of a variable x. This will reduce complexity.

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