Q2. Raghav, Chandni, and Sohumpurchased pens, erasers, and pencils. 0/3 Raghav said, "Seven pens and five erasers costthe same as six pencils. Chandni said, "Fourpens and nine pencils cost the same as fiveerasers. Sohum said, " cost of six pencils andthree erasers is same as four pens. It seemsthat one of them has made wrong statement.Who committed error in calculations and gave
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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