Raghav, Chandni, and Sohum purchased pens, erasers, and pencils. Raghav said, “Seven pens and five erasers cost the same as six pencils. Chandni said, "Four pens and nine pencils cost the same as five erasers. Sohum said, " cost of six pencils and three erasers is the same as four pens. It seems that one of them has made the wrong statement. Who committed error in calculations and gave the wrong statement?
Answers
Given : Raghav said, Seven pens and five erasers cost the same as six pencils.
Chandni said, "Four pens and nine pencils cost the same as five erasers.
Sohum said, " cost of six pencils and three erasers is same as four pens
one of them has made wrong statement
To Find : Who committed error in calculations
Solution:
Pen cost = x
Pencil cost = y
eraser cost = z
Raghav said, Seven pens and five erasers cost the same as six pencils.
=> 7x + 5z = 6y
Chandni said, "Four pens and nine pencils cost the same as five erasers.
=> 4x + 9y = 5z
Sohum said, " cost of six pencils and three erasers is same as four pens
=> 6y + 3z = 4x
Case 1 : Assume Raghav did not make error
Raghav
7x + 5z = 6y => 5z = 6y - 7x
Chandni
4x + 9y = 5z
Substituting 5z from raghav
=> 4x + 9y = 6y - 7x
=> 11x + 3y = 0 which is not possible
Hence Chandni made error
Sohum
6y + 3z = 4x
Substituting 6y from raghav
7x + 5z + 3z = 4x
=> 8z + 3x = 0 which is not possible
Hence Sohum also made error
so This case is not possible as 2 person made error.
so Raghav must have made error
Still lets check all possible cases to verify
Case 2 : Assume Chandni did not make error
Chandni
4x + 9y = 5z => 4x = 5z - 9y
Raghav
7x + 5z = 6y
substitute 5z from Chandni
7x + 4x + 9y = 6y
=> 11x + 3y = 0 which is not possible
Hence Raghav made error
Sohum
6y + 3z = 4x
Substituting 4x from Chandni
6y + 3z = 5z - 9y
=> 15y = 2z which is possible
Hence only Raghav made error
So this is possible that Raghav made an error
Case 3 :
Sohum did not make error
6y + 3z = 4x => 6y = 4x - 3z
Raghav :
7x + 5z = 6y
substitute 6y from Sohum
=> 7x + 5z = 4x - 3z
=> 3x + 8z = 0 which is not possible
Hence Raghav made error
Chandni
4x + 9y = 5z
substitute 4x from Sohum
6y + 3z + 9y = 5z
=> 15y = 2z which is possible
Hence Raghav has made error
Raghav Committed error in calculations
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