Question

Amita bought hair dryer for Rs 900 and sold it at a gain of 10% . She sold another hair dryer at 5% loss which she bought for Rs 1200. On the whole transaction she has a

Answer 1

Answer:

gain of Rs 30       ;   gain% = 10/7 %

Step-by-step explanation:

   Case 1:   Amita bought hair dryer for Rs 900 and sold it at a gain of 10%.

CP = Rs 900        ;  gain% = 10%

   Using, gain% = (SP - CP)/CP * 100%

⇒ 10% = (SP - 900)/900 * 100%

⇒ 90 = SP  - 900

⇒ 900 + 90 = SP

⇒ 990 = SP

   

       Case 2:     She sold another hair dryer at 5% loss which she bought for Rs 1200.

  CP = Rs 1200   ; loss = 5%

            Using,  loss% = (CP - SP)/CP * 100%

⇒ 5% = (1200 - SP)/1200 * 100%

⇒ 60 = 1200 - SP

⇒ SP = 1140

   Total cost = 900 + 1200 = 2100

   Total SP = 990 + 1140 = 2130

Clearly, SP > CP,  there's a gain

gain = 2130 - 2100 = 30

gain % = (gain/CP) * 100%

             = 30/2100 * 100%

             = 10/7 %

Answer 2

Question

Amita bought hair dryer for Rs 900 and sold it at a gain of 10% . She sold another hair dryer at 5% loss which she bought for Rs 1200. On the whole transaction she has a

Solution

1st hair dryer

CP = ₹900

Gain%(r) = 10%

SP = ?

Gain = ??

$\bf{SP=\Bigg(1+ \dfrac{r}{100}\Bigg)CP}$

$\sf\implies \: SP=\Bigg(1+ \dfrac{10}{100}\Bigg)900$

$\sf\implies\:SP=\Bigg(\dfrac{11}{10}\Bigg)900$

$\sf\implies{SP= \dfrac{11}{10}×900}$

$\sf\implies{SP = ₹990}$

Gain = SP - CP

Gain = ₹990-₹900

Gain = ₹90

2nd hair dryer

CP = ₹1200

Loss% = 5%

SP = ?

Loss = ??

$\bf{SP=\Bigg(1 - \dfrac{r}{100}\Bigg)CP}$

$\sf\implies{SP=\Bigg(1 - \dfrac{5}{100}\Bigg)1200}$

$\sf\implies{SP=\Bigg(\dfrac{19}{20}\Bigg)1200}$

$\sf\implies{SP= \dfrac{19}{20}×1200}$

$\sf\implies{SP=₹1140}$

Loss = CP - SP

Loss = ₹1200 - ₹1140

Loss = ₹60

On whole transaction

CP = ₹900 + ₹1200 = ₹2100

SP = ₹990 + ₹1140 = ₹2130.

Gain = ₹90 - ₹60

Gain = ₹30.

Gain% = $\sf\dfrac{Gain}{CP}×100$

Gain% = $\sf\dfrac{30}{2100}×100$

Gain% = $\sf\dfrac{30}{21}\%$

Gain% = $\sf\dfrac{10}{7}\%$

Gain% = 1.42%

Therefore

• Gain = ₹30
• Gain% = 10/7% or 1.42%.