Question

by selling tow tables for Rs. 1200 each, a man gains 10% on one and loses 10% on the other. find hhis gain or loss percent in the whole transaction

Answer 1

Answer:

Step-by-step explanation:

Given,  

SP of 1 table = Rs.1200

profit% = 10  

CP = fraction numerator 100 over denominator 100 plus P percent sign end fraction cross times S P

= fraction numerator 100 over denominator 100 plus 10 end fraction cross times 1200

= 100 over 110 cross times 1200

CP = 1090.90

 

 

Loss = 10%

CP = fraction numerator 100 over denominator 100 minus L percent sign end fraction cross times S P

= fraction numerator 100 over denominator 100 minus 10 end fraction cross times 1200

= 100 over 90 cross times 1200

CP = 1333.33

 

Total CP of 2 tables = 1090.90 + 1333.33 = Rs.2424.23

 

Total SP of 2 tables = 1200 × 2 = Rs.2400

 

CP > SP, so a loss is incurred

 

Loss = CP - SP  

= 2424.23 - 2400

=Rs.24.23

 

Loss% = fraction numerator L cross times 100 over denominator C P end fraction

= fraction numerator 24.23 cross times 100 over denominator 2424.23 end fraction

= 0.99 approximately equal to 1%

Hence, a loss of approximately 1% was incurred.

Answer 2

Given :

Selling price of each table : ₹1200

Gain percent of one table : 10%

Loss percent of other table : 10%

To find :

The gain or loss percentage on whole transaction.

Solution :

First, we should find the cost price of both tables.

Cost price of first table :

$\sf \dashrightarrow \dfrac{100}{(100 + Gain\%)} \times SP$

$\sf \dashrightarrow \dfrac{100}{(100 + 10)} \times 1200$

$\sf \dashrightarrow \dfrac{100}{110} \times 1200$

$\sf \dashrightarrow \dfrac{10}{11} \times 1200$

$\sf \dashrightarrow \dfrac{1200 \times 10}{11} = \dfrac{12000}{11}$

$\sf \dashrightarrow \cancel \dfrac{12000}{11} = 1090.9$

Cost price of second table :

$\sf \dashrightarrow \dfrac{100}{(100 - Loss\%)} \times SP$

$\sf \dashrightarrow \dfrac{100}{(100 - 10)} \times 1200$

$\sf \dashrightarrow \dfrac{100}{90} \times 1200$

$\sf \dashrightarrow \dfrac{10}{9} \times 1200$

$\sf \dashrightarrow \dfrac{1200 \times 10}{9} = \dfrac{12000}{9}$

$\sf \dashrightarrow \cancel \dfrac{12000}{9} = 1333.3$

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

Total cost price :

$\sf \dashrightarrow 1090.9 + 1333.3$

$\dashrightarrow$₹$\sf 2424.2$

Total selling price :

$\sf \dashrightarrow 1200 + 1200$

$\dashrightarrow$₹$\sf 2400$

Now, we can find the loss percentage.

Loss percentage :

$\sf \dashrightarrow \dfrac{CP - SP}{Cost \: price} \times 100$

$\sf \dashrightarrow \dfrac{2424.2 - 2400}{2424.2} \times 100$

$\sf \dashrightarrow \dfrac{24.2}{2424.2} \times 100$

$\sf \dashrightarrow \dfrac{242}{24242} \times 100$

$\sf \dashrightarrow \dfrac{121}{12121} \times 100$

$\sf \dashrightarrow \dfrac{121 \times 100}{12121} = \dfrac{12100}{12121}$

$\sf \dashrightarrow \cancel \dfrac{12100}{12121} = 0.99$

Hence, the loss percentage on whole transaction is 0.99%.