Question

A LADY BUYS SOME PENCILS FOR ₹3 AND AN EQUAL NUMBER FOR ₹6 .SHE SELLS THEM FOR ₹7. FIND HER GAIN OR LOSS %.​

Answer 1

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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