Question

A radio is sold for Rs.990 at a profit of 10%.
What would have been the gain or loss %, had
it been sold for Rs.890?
a) Loss, 10% b) Gain, 12%
c) Loss, 12% d) Loss, 1%​

Answer 1

Given :

• Selling price of radio at profit of 10% is Rs.990

To Find :

• Gain or loss% when the selling price of the radio is Rs.890

Solution :

Profit% of an article is given by ,

$\\ \star \: {\boxed{\sf{\purple{profit\% = \frac{(SP - CP) \times 100}{CP} }}}}$

We have ,

• Profit% = 10%
• Selling price (SP) = Rs.990
• Cost price (CP) = ?

Substituting the values we have ,

$\\ : \implies \sf \: 10 = \frac{(990 -CP) \times 100 }{CP}$

$\\ : \implies \sf \: 10CP = (990 - CP) \times 100$

$\\ : \implies \sf \: 10CP = 99000 - 100CP$

$\\ : \implies \sf \: 10CP + 100CP = 99000$

$\\ : \implies \sf \: 110CP = 99000$

$\\ : \implies \sf \: CP = \frac{99000}{110}$

$\\ : \implies{\boxed{\red{\sf{ \:CP = Rs.900 }}}}$

Since the change in Cost price is not mentioned . The Cost price will remain constant i.e , Rs.900

Selling price = Rs.890 [Given]

Here (SP) < (CP)

So , There must be a loss.

Loss% of an article is given by ,

$\\ \star \: {\boxed{\sf{\purple{loss\% = \frac{(CP - SP ) \times 100}{CP} }}}}$

Substituting the values ,

$\\ : \implies \sf \: loss\% = \frac{(900 - 890) \times 100}{900}$

$\\ : \implies \sf \: loss\% = \frac{10 \times 100}{900}$

$\\ : \implies{\boxed{\pink{\sf{loss\% \approx \: 1\% }}}} \: \bigstar$

Therefore , The loss% is 1% . Hence , Option(D) is the required answer.

Answer 2

☆Answer☆

Given,

Selling price of radio at profit of 10% is Rs.990.

• Profit = 10%

• Selling price (SP) = Rs.990

• Cost price (CP) = ?

From the formula

Profit% = (SP-CP)×100/CP

10 = (990-CP)×100/CP

10CP = (990−CP)×100

10CP = 99000−100CP

10CP+100CP = 99000

110CP = 99000

CP = 99000/110

CP = Rs.900

[Here CP > SP]

So, we have loss.

Loss% = (CP-SP)×100/CP

= (900-890)×100/900

= 10×100/900

= 1 %

Loss% = 1%

Correct option is (d).

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