Question

An owner of a motor garage bought two second hand cars for Rs.1,18,000 each. He sold one car at a loss of 15% and the other at a profit of 30%. Find his total loss or profit % in the whole transaction.​

Answer 1

Given :-

• Cost price of each car = R.s 118000

To Find :-

• Total loss or gain in the whole transaction = ?

Solution :-

• To calculate his loss or gain in the whole transaction at first we have to find out total selling price and cost price of the cars then calculate his loss or gain %.

Calculation for 1st car :-

• CP = 118000. L = 15%

⇢ SP = (100 - L%)/100 × CP

⇢ SP = (100 - 15)/100 × 118000

⇢ SP = 85/100 × 118000

⇢ SP = 85 × 1180

⇢ SP = 100300

Calculation for 2nd car :-

• CP = 118000. P = 30 %

⇢ SP = (100 + P%)/100 × CP

⇢ SP = (100 + 30)/100 × 118000

⇢ SP = 130/100 × 118000

⇢ SP = 130 × 1180

⇢ SP = 153400

Now calculate total CP and SP :-

⇢ Total CP of car = 118000 + 118000

⇢ Total CP of car = Rs. 236000

⇢ Total SP of car = 100300 + 153400

⇢ Total SP of Car = Rs. 253700

Above the calculation we can easily say that the owner of the motor garage will have profit because the amount of SP is greater than CP (SP>CP).

⇢ P% = (SP - CP)/CP × 100

⇢ P% = (253700 - 236000)/236000 × 100

⇢ P% = 17700/236000 × 100

⇢ P% = 17700/2360

⇢ P% = 7.5%

Hence, the owner has profit of 7.5%.

Answer 2

★ Solution :-

First, we should find the selling price of both cars.

Selling price of first car :-

$\sf \leadsto \dfrac{(100 - Loss\%)}{100} \times CP$

$\sf \leadsto \dfrac{(100 - 15)}{100} \times 118000$

$\sf \leadsto \dfrac{85}{100} \times 118000$

$\sf \leadsto \dfrac{17}{20} \times 118000$

$\sf \leadsto \dfrac{17 \times 118000}{20} = \dfrac{2006000}{20}$

$\sf \leadsto \cancel \dfrac{2006000}{20} = 100300$

Selling price of second car :-

$\sf \leadsto \dfrac{(100 + Profit\%)}{100} \times CP$

$\sf \leadsto \dfrac{(100 + 30)}{100} \times 118000$

$\sf \leadsto \dfrac{130}{100} \times 118000$

$\sf \leadsto \dfrac{13}{10} \times 118000$

$\sf \leadsto \dfrac{13 \times 118000}{10} = \dfrac{1534000}{10}$

$\sf \leadsto \cancel \dfrac{1534000}{10} = 153400$

Now, we should find the total cost and selling price.

Total cost price :-

$\sf \leadsto 118000 + 118000$

$\sf \leadsto Rs.236000$

Total selling price :-

$\sf \leadsto 100300 + 153400$

$\sf \leadsto Rs.253700$

We can see that the selling price is greater than cost price. So,

Profit percentage :-

$\sf \leadsto \dfrac{SP - CP}{CP} \times 100$

$\sf \leadsto \dfrac{253700 - 236000}{236000} \times 100$

$\sf \leadsto \dfrac{17700}{236000} \times 100$

$\sf \leadsto \dfrac{177}{2360} \times 100$

$\sf \leadsto \dfrac{177}{118} \times 5$

$\sf \leadsto \dfrac{177 \times 5}{118} = \dfrac{885}{118}$

$\sf \leadsto \cancel \dfrac{885}{118} = 7.5$

Therefore, the owner gains a profit of 7.5% on whole transaction.