Question

By selling two electric room heaters for Rs 3240 each,harsh makes profit of 8% on one and a loss of 10% on the other.find the total loss or gain%.
ANS 20÷11

Answer 1

Answer: Since you've already provided the answer, here's the worked out solution.

Step-by-step explanation:

Let 'x' be the cost price of heater on which a profit of 8% was made. Then,

$x+\frac{8}{100} x=3240$

⇒$\frac{108x}{100} =3240$

⇒$x=3000$

Thus, the cost price of this heater is Rs.3000

Now, let 'y' be the cost price of heater on which a loss of 10% was made. Then,

$y-\frac{10}{100}y=3240$

⇒$\frac{90y}{100}=3240$

⇒$y=3600$

Thus, cost price of the second heater is Rs.3600

Now, total cost price = 3000+3600 = Rs.6600

whereas, total selling price = 3240+3240 = Rs.6480

Clearly, this was a situation of loss(poor Harsh :p). Now,

Loss = 6600-6480 = Rs.120

And loss % = Loss x 100/Cost Price

Loss % = $\frac{120}{6600} X 100 = \frac{20}{11}$

which, as you've mentioned is the answer.

Answer 2

Answer:

The Loss % in the whole transaction is $\sf{\dfrac{20}{11}\%}$

Step-by-step explanation:

Given :

Selling Price of two electric heaters each = Rs. 3240

Profit made on one = 8%

Loss Made = 10%

To find :

Total Loss or Gain %.

Solution :

$\large{\textsf{\underline{\underline{Case I}}}}$

Here -

• Selling Price = Rs. 3240
• Profit % = 10%
• Cost Price = ??

$\bigstar\:{\boxed{\sf\:{CP = \frac{100}{(100 + profit\%)} \times SP}}}$

$\sf{\longrightarrow} \: CP = \dfrac{100}{(100 + 8\%)} \times 3240 \\ \\ \sf{\longrightarrow} \: CP = \dfrac{100}{108} \times 3240 \\ \\ \sf{\longrightarrow} \: CP = \dfrac{324000}{108} \\ \\ \sf{\longrightarrow} \: CP = 3000$

Cost Price of first heater = Rs. 3000

$\rule{300}{1.5}$

$\large{\textsf{\underline{\underline{Case II}}}}$

Here -

• Selling Price = Rs. 3240
• Loss % = 10%
• Cost Price = ??

$\bigstar\:{\boxed{\sf\:{CP = \frac{100}{(100 - Loss \%)} \times SP}}}$

$\sf{\longrightarrow}\:CP = \dfrac{100}{(100 - Loss \%)} \times SP \\ \\ \sf{\longrightarrow}\:CP = \dfrac{100}{100 - 10\%} \times 3240 \\ \\ \sf{\longrightarrow}\:CP = \dfrac{100}{90} \times 3240 \\ \\ \sf{\longrightarrow}\:CP = \dfrac{324000}{90} \\ \\ \sf{\longrightarrow}\:CP = 3600$

Cost Price of second heater = Rs. 3600

$\rule{300}{1.5}$

${\textbf{Total Gain or Loss - }}$

✯ $\textsf{Total Selling Price =}$

$\sf{\longrightarrow}\:3240 + 3240 \\ \sf{\longrightarrow}\:6480$

✯ $\textsf{Total Cost Price = }$

$\sf{\longrightarrow}\:3000 + 3600 \\ \sf{\longrightarrow}\:6600$

6600 > 6480

Cost Price > Selling Price

$\therefore$ It is a Loss !

$\rule{300}{1.5}$

$\textsf{\large{\underline{Loss -}}}$

★ $\boxed{\sf{Cost\:Price-Selling\: Price}}$

$\sf{\longrightarrow}\:6600 - 6480 \\\sf{\longrightarrow}\: 120$

Loss = Rs. 120

$\rule{300}{1.5}$

$\textsf{\large{\underline{Loss \% -}}}$

★ $\boxed{\sf\:{Loss\% = \frac{Loss}{CP} \times 100}}$

$\sf{\longrightarrow} \: Loss\% = \dfrac{120}{6600} \times 100 \\ \\ \sf{\longrightarrow} \:Loss\% = \frac{12000}{6600} \\ \\ \sf{\longrightarrow} \:Loss\% = \frac{20}{11}$

$\therefore$ The Loss % in the whole transaction is $\sf{\dfrac{20}{11}\%}$