Rachel says "7 pens and five erasers cost the same as 6 pencils."
Chan says "4 pens and 9 pencils cost the same as 5 erasers"
Sue says "6 pencils and 3 eraser cost the same as 4 pens"
Only one is lying can you tell us who?
Chan says "4 pens and 9 pencils cost the same as 5 erasers"
Sue says "6 pencils and 3 eraser cost the same as 4 pens"
Only one is lying can you tell us who?
Add an Answer
More Questions From This User See All
Answers & Comments
Verified answer
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
Answer:
Hence Rachal has made error.
Solution:
Given is ,
if we assume
pen cost = x
pencil cost = y
eraser = z
then
according to Rachel,
7x+5z = 6y
according to Chan,
4x + 9y = 5 z
according to sue,
6x + z = 4x
case1:
If Rachal did not make error then
7x+5z = 6y
5z = 6y_7X
chan
4x + 9y = 5 z
when we substitute 5z frome Rachal
4x + 9y = 6y-7x
=11x+3y=0
Therefore chan made an error
When we apply same calculation on Sue he also made an error.
We can say Rachal make an error.
Let check other possiblities
Case 2:
Assume Chan did not make error
Chan
4x + 9y = 5z
=>4x=5z-9y
Rachal
7x + 5z = 6y
substitute 5z from Cha
7x + 4x + 9y = 6y
=>11x+3y=0 which is not possible
Hence Rachal made error
Sue
6y + 3z = 4x
Case 3:
So did not make error
6y+3z=4x=>6y=4x-3z
Rachal :
7x + 5z = 6y
substitute 6y from Sue
=>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 Rachal has made error
Rachal made calculating mistake.