A lady buys some pencil at rs.6 and the same equal to the RS.3.If she sell it at Rs.7.then find its loss or gain percent?
Answers
Given :-
- CP of some pencils = Rs.3
- CP of same Number of pencil = Rs.6
- SP of all pencile = Rs.7 .
To Find :-
- Total gain or Loss % ?
Solution :-
Let us assume that, the lady by x number of pencils in both cases .
so,
→ CP of x pencils = Rs.3
then,
→ CP of each pencil = Rs. (3/x) ------------ Eqn.(1)
similarly,
→ CP of x pencils = Rs.6
then,
→ CP of each pencil = Rs. (6/x) ----------- Eqn.(2)
now,
→ Total pencils she sell = x + x = 2x pencils .
and,
→ SP of 2x pencils = Rs.7
then,
→ SP of each pencils = Rs.(7/2x) ----------- Eqn.(3)
now, we know that,
If SP > CP . we have Profit .
if SP < CP . we have Loss.
so,
→ Eqn.(3) > Eqn.(1)
→ (7/2x) > (3/x)
→ SP > CP
therefore,
→ Profit = SP - CP = (7/2x) - (3/x) = (7 - 2*3)/2x = (7 - 6)/2x = Rs.(1/2x)
→ Profit % = (Profit in Rs. * 100) / CP = [(1/2x) * 100]/(3/x) = (x * 100) / (2x * 3) = (50/3) % .
similarly,
Eqn.(3) < Eqn.(2)
→ (7/2x) < (6/x)
→ SP < CP
therefore,
→ Loss = CP - SP = (6/x) - (7/2x) = (2*6 - 7)/2x = (12 - 7)/2x = Rs.(5/2x)
→ Loss % = (Loss in Rs. * 100) / CP = [(5/2x) * 100]/(6/x) = (5 * x * 100) / (2x * 6) = (125/3) % .
hence,
→ Total gain or Loss % = (50/3) + {-(125/3)} (For loss we use -ve sign)
→ Total gain or Loss % = (50/3) - (125/3)
→ Total gain or Loss % = (50 - 125)/3
→ Total gain or Loss % = (-75/3)
→ Total gain or Loss % = (-25)% .
Here -ve sign shows that , the lady has a Loss in overall.
Hence, Her Total Loss % is 25 .
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