Question

A man sold two articles at Rs 25920 each.These were sold at 8% gain and 4% loss respectively. Find the gain or loss per cent in the whole transaction.

Answer 1

Answer:

He will gain 1.647%

Step-by-step explanation:

Given data

Two articles sold at Rs .25920

one is sold at 8% gain, and another one is sold at 4% loss

Here we need to find gain or loss in the whole process

Article 1, selling price = 25920 Rs

     gained percentage = 8%

⇒  cost price on Article 1 =  100 × $[ \frac{25920}{100+8} ]$    

                                            =  100 × $[ \frac{25920}{108} ]$  

                                            = 100 × 240 = 24,000 Rs

Article 2, selling price  = 25920 Rs

         loss percentage  =  4%  

⇒ cost price on Article 2 =  100 × $[ \frac{25920}{100-4} ]$  

                                          =  100 × $[\frac{25920}{96}]$  

                                          = 100 × 270 =27,000 Rs

⇒ cost price of both Articles = 24000 + 27000 = 51,000 Rs

⇒ from given data selling price of both Articles

                              = 25920 + 25920 = 51,840 Rs

⇒ selling price > cost price, then it is profitable for him

⇒ therefore profit = selling price - cost price

                               = 51840 -51000 = 840 Rs

⇒ gain percentage  =  (gain× 100) ÷ cost price

                                  =  (840 × 100) / 51000

                                  = 84000/ 51000

                                  = 1.647 %

Answer 2

Gain per cent in the whole transaction is about 1.647 % if a man sold two articles at Rs 25920 each and were sold at 8% gain and 4% loss respectively.

Given:

• A man sold two articles at Rs 25920 each
• Sold at 8% gain and 4% loss respectively

To Find:

• The gain or loss per cent in the whole transaction.

Solution:

• SP = CP + GAIN
• SP  = CP - LOSS

Step 1:

Assume that cost price of items are x and  y

Step 2:

Calculate 8 % gain on x

= (8/100)x= 0.08x

Step 3:

Add gain in CP and equate with SP

x + 0.08x  = 25920

=> 1.08x = 25920

=> x =  24000

Step 4:

Calculate 4 % loss on y

= (4/100)y

= 0.04y

Step 5:

Subtract loss from CP and equate with SP

y - 0.04y  = 25920

=> 0.96y = 25920

=> y =  27000

Step 6:

Calculate total CP and Total SP

Total CP = 24000 + 27000 = 51000

Total SP = 25920 + 25920  = 51840

As SP > CP Hence, Gain

Step 7:

Calculate Gain and Gain %

Gain = 51840 - 51000 = Rs 840

Gain % = (840/51000) x 100

Gain % ≈ 1.647

Gain per cent in the whole transaction is about 1.647 %