Question

1.
A man sold two jeans at Rs. 800 each. On one he gains 10% and on the other he loses 15%.
How much does he gain or loss in the whole transaction?
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Answer 1

Given

SP of both jeans = 800

Gain on 1 = 10%

loss on the other = 15%

To Find

We have to find the total loss/gain%

Solution:-

First we have to find out the CP of both jeans

Let the CP of first jeans be x of gain 10%

$\sf\ x+10\%of \ x= 800\\ \\ \\:\implies\sf\ x+ \dfrac{1\cancel0}{10\cancel0}\times x=800\\ \\ \\:\implies\sf\ \dfrac{10x+x}{10}=800\\ \\ \\:\implies\sf\ 11x= 8000\\ \\ \\:\implies\sf\ x=\cancel{\dfrac{8000}{11}}\\ \\ \\:\implies\sf\ x= CP= 727.27------(i)$

Now CP of 2nd jeans of loss 15%

let CP be y

$\sf\ y-15\%of \ y= 800\\ \\ \\:\implies\sf\ y- \dfrac{15}{100}\times y=800\\ \\ \\:\implies\sf\ \dfrac{100y-15y}{100}=800\\ \\ \\:\implies\sf\ 85y= 80000\\ \\ \\:\implies\sf\ y=\cancel{\dfrac{80000}{85}}\\ \\ \\:\implies\sf\ y= CP= 941.17------(ii)$

So, we have

Total CP= eq.(i)+eq.(ii)

=> 727.27+941.17

=> 1668.44

Now

$\bullet\sf\ Total\ CP= 1668.44\\ \\ \bullet\sf\ Total \ SP=1600\\ \\ \sf\ \ SP<CP\ it's\ Loss\\ \\ \\ \sf\ Loss\%= \dfrac{CP-SP}{CP}\times 100\%\\ \\ \\ :\implies\sf\ Loss\%= \dfrac{1668.44-1600}{1668.44}\times 100\%\\ \\ \\ :\implies\sf\ Loss\%= \dfrac{68.44\times 100\%}{1668.44}\\ \\ \\ :\implies\sf\ Loss\%= \cancel{\dfrac{6844\%}{1668.44}}\\ \\ \\ :\implies\sf\underline{\boxed{\sf\ Loss\%= 4.10\%}}$

Answer 2

Answer:

Given :-

SP of both jeans = 800

Gain on 1 = 10%

loss on the other = 15%

To Find :-

Total gain or loss %

SoluTion :-

At first

Total SP = 2(800) = ₹1600

Now,

Let the first CP be x

x + 10% of x = 800

x + 10/100 × x = 800

x + 1/10 × x = 800

Now,

10 × x + x/10 = 800

10x + x/10 = 800

10x + x = 800 × 10

11x = 8000

x = ₹727 = CP of the first jeans

Now,

Let the other CP be y

Now,

y - 15% of y = 800

y - 15/100 × y = 800

100 × y - 15 × y/100 = 800

100y - 15y/100 = 800

85y/100 = 800

85y = 100 × 800

85y = 80000

y = 941.17

Clearly

Total CP =

727.27+941.17

1668.44

Now,

SP < CP = Loss

Loss% = 1668.4 - 1600/1668.4 × 100

Loss% = 68.44/1668.4 × 100

Loss% = 4.1%