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The ratio of selling price of article $A, B, C$ is $8 : 9 : 5$ and ratio of percentage profit is $8 : 7 : 14$ respectively. If the profit percentage of $A$ is $14.28 %$ and the cost price of $B$ is Rs. $400$ , what is the overall percentage gain?

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12.78%

15.78%

14.78%

13.78%

answer is D.

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Detailed Solution

Given,
Selling price of article

A, B

and

C

is in ratio

8 : 9 : 5

.
The profit percentage of

A

14.28 %

and the cost price of

B

is Rs.

400

.
Let the selling price be

8 y, 9 y

and

5 y

.
Profit percentage are in ratio

= 8 : 7 : 14

Let their profit percentage be

8 x %, 7 x %

and

14 x %

.
A's profit percent

= 14.28 %

\Rightarrow 8 x % = 14.28 %

\Rightarrow x % = \frac{14.28}{8}

\Rightarrow x % = 1.78

B^{'} s

profit percent,

B % = 7 x %

\Rightarrow B % = 7 \times 1.78

\Rightarrow B % = 12.50 %

C^{'} s

profit percentage,

C % = 14 x

\Rightarrow C % = 14 \times 1.78

\Rightarrow C % = 25 %

We know,
Profit =

\frac{Profit %}{100} \times CP

\Rightarrow

Profit of B =

\frac{12.50}{100} \times 400 = Rs . 50 .

Cost price of

B =

Rs.

400

∴

Selling price of B,
SP = CP+ profit

\Rightarrow

S.P=400 +50

\Rightarrow

S.P=Rs.450

\Rightarrow 9 y = 450

[from given]

\Rightarrow y = 50

Selling price of

A

,
S.P

= 8 y

\Rightarrow S . P = 8 \times 50

\Rightarrow

S.P=Rs.

400

SP of

C

,
S.P

= 5 y

\Rightarrow S . P = 5 \times 50

\Rightarrow

S.P=Rs.

250

Total SP

= 450 + 400 + 250

\Rightarrow

Total SP=Rs.

1100

Let CP of

A = a

.
We know,

S . P . = C . P + \frac{Profit %}{100} \times C . P .

\Rightarrow C . P . = S . P . - \frac{Profit %}{100} \times C . P

Then.

\Rightarrow a = 400 - \frac{14.28}{100} \times

a

\Rightarrow a = 400 - \frac{14.28 a}{100}

\Rightarrow 100 a = 40000 - 14.28 a

\Rightarrow 114.28 a = 40000

\Rightarrow a =

Rs.

350

Let CP of

C = c

. Then,

\Rightarrow c = 250 - \frac{25}{100} \times

c

\Rightarrow c = 250 - \frac{1}{4} c

\Rightarrow 5 c = 1000

\Rightarrow c =

Rs.

200

Total CP

= 400 + 350 + 200

\Rightarrow

Total CP=Rs.

950

We know,
Total Profit = Total S.P. - Total C.P.
Profit

= 1100 - 950

\Rightarrow Profit = Rs . 150

Total profit % will be,
Profit%

= \frac{Total profit}{Total CP} \times 100

\Rightarrow

Profit%

= \frac{150}{950} \times 100

\Rightarrow Profit % = 15.78 %

Thus, the overall profit will be 15.78%.
Therefore, the correct option is 4.

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