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CAT 2001 | Question: 46

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A change making machine contains $1$ rupee, $2$ rupee and $5$ rupee coins. The total number of coins is $300.$ The amount is Rs. $960.$ If the number of $1$ rupee coins and the number of $2$ rupee coins are interchanged, the value comes down by Rs. $40.$ The total number of $5$ rupee coins is

  1. $100$
  2. $140$
  3. $60$
  4. $150$

1 Answer

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2 2 votes

Let X=Number of 1 Rupee coins

Y= Number of 2 Rupee coins

Z= Number of 5 Rupee coins

 

Given,Number of coins ( X + Y + Z ) =300$\cdots$(1)

1 X + 2 Y + 5 Z=960$\cdots$(2) 

 

Number of 1 Rupee coins and the number of 2 Rupess coins are interchenged.So,

2 X +  Y + 5 Z = 960 - 40 = 920 $\cdots$(3)

 

From (1) ,(2) and (3)

Y - X = 40$\cdots$(4)

Y + 4 Z = 660$\cdots$(5)

X + 4 Z = 620$\cdots$(6)

 

Put the value of  X and Y from (5) and (6) in (1)

620 - 4 Z - 660 - 4 Z + Z = 300

Z = 140

 

Hence,Option (2)140 is the correct choice.

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