Question

A lady buys some pencils for rs 3 and an equal number for rs.6 she sells them for rs.7. Find her gain or loss percentage

Answer 1

_________________________________________

$\underline{\underline{\huge{\textbf{Solution:}}}}$

Given,

A lady buys some pencils for rs 3
and an equal number for rs.6

Then she sells them for rs.7.

Gain or Loss Percentage = ?

$\underline{\large{\textsf{Step-1:}}}$
Assume No. of pencils bought as a Variable

Let No. of 3 Rs. Pencils bought be x
and No. of 6 Rs. Pencils bought = x
(Given that the lady bought equal number of 3 Rs. pencils and 6 Rs. pencils)

$\underline{\large{\textsf{Step-2:}}}$
Express the Cost Price of 3Rs. Pencils in terms of the variable.

Cost Price of 'x' 3 Rs. pencils = No. of pencils × Cost of each Pencil

$\implies Cost\: price\: of\: 'x' 3\: Rs.\: Pencils = 3x$

$\underline{\large{\textsf{Step-3:}}}$
Express the Cost Price of 6Rs. Pencils in terms of the variable.

Cost Price of 'x' 6 Rs. pencils = No. of pencils × Cost of each Pencil

$\implies Cost\: Price\: of\: 'x' 6\: Rs.\: Pencils = 6x$

$\underline{\large{\textsf{Step-4:}}}$
Find the Cost Price of all the pencils bought by the lady

Cost Price of all the Pencils (CP) = Cost Price of 'x' 3 Rs. pencils + Cost Price of 'x' 6 Rs. pencils

$\implies CP = 3x+6x$

$\implies Cost\: Price\: of\: all\: Pencils,\: CP = 9x$

$\underline{\large{\textsf{Step-5:}}}$
Express the Selling Price of 3 Rs. Pencils in terms of variable

Selling Price of 'x' 3 Rs. pencils = No. of pencils × Selling Price of each Pencil

$\implies Selling\: of\: 'x' 3\: Rs.\: Pencils = 7x$

$\underline{\large{\textsf{Step-6:}}}$
Express the Selling Price of 6 Rs. Pencils in terms of variable

Selling Price of 'x' 6 Rs. pencils = No. of pencils × Selling Price of each Pencil

$\implies Selling\: of\: 'x' 3\: Rs.\: Pencils = 7x$

$\underline{\large{\textsf{Step-7:}}}$
Find the Selling Price of all the pencils sold by the lady

Selling Price of all the Pencils (SP) = Selling Price of 'x' 3 Rs. pencils + Selling Price of 'x' 6 Rs. pencils

$\implies SP = 7x+7x$

$\implies Selling\: Price\: of\: all\: Pencils,\: SP = 14x$

$\underline{\large{\textsf{Step-8:}}}$
Check whether there is Gain or Loss

$\textsf{There will be Gain , when SP > CP}$

$\textsf{There will be Loss , when SP < CP}$

Here,
SP = 14x
CP = 9x

$SP > CP$

$\therefore$
There will be Gain

$\underline{\large{\textsf{Step-9:}}}$
Find the Gain

$\textsf{Gain = Selling Price (SP) - Cost Price (CP)}$

By Substituting

Gain = 14x - 9x

$\implies Gain = 5x$

$\underline{\large{\textsf{Step-10:}}}$
Calculate the $Gain\%$

We have,
$\textsf{Gain\% = \dfrac{Gain}{CP} \times 100 }$

$\implies Gain\% = \frac{5x}{9x} \times 100$

$\implies Gain\% = \frac{5}{9} \times 100$

$\implies Gain\% = 0.555 \times 100$

$\implies Gain\% = 55.5\%$

$\therefore$
$\textsf{Gain Percentage = \underline{55.5\%}}$
          
 _________________________________________

Answer 2

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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