Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

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?

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

12.78%

15.78%

14.78%

13.78%

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!