Question

If the P of 13 bats is Rs 390. What is the price when it is sold at $10\% $ loss?
A) Rs.200
B) Rs. 300
C) Rs. 350
D) Rs.351

Answer 1

Hint: In order to solve this question we will first calculate loss by making use of formula \[Loss\% = \dfrac{{Loss}}{{\operatorname{Cos} t\,price}} \times 100\] then we will calculate the price of 13 bats sold at $10\% $ loss by subtracting loss from the present cost price of the 13 bats.

Complete step by step answer:
Given, P of 13 bats is Rs 390. Thus, the cost price of the 13 bats is Rs 390.
 In order to find the selling price of the 13 bats when it’s sold at $10\% $ loss we should first find out the loss that will be incurred after selling the bats at $10\% $ loss by substituting the given values in the above formula.
Thus, $10 = \dfrac{{Loss}}{{390}} \times 100$
 Now we can reduce the right-hand side of the equation by eliminating one zero from the numerator and denominator. Therefore, our equation becomes $10 = \dfrac{{Loss}}{{39}} \times 10$.
 Now we can bring 39 from the denominator of the left-hand side to the numerator of the right-hand side because when the denominator of one side is brought on another side it becomes the numerator of that side and vice versa. Therefore, our equation becomes $10 \times 39 = Loss \times 10$.
Now our aim is to bring loss on one side and all the numbers on another side. So, in order to achieve this, we will divide the right-hand side by 10 since 10 is multiplied on the left-hand side; it has to be divided if it is moved on another side. Therefore, our equation becomes $\dfrac{{10 \times 39}}{{10}} = Loss$.
Now we will reduce the left-hand side by eliminating 10 from the numerator and as well as the denominator. Therefore, our equation becomes Loss= 39.
Now, it is clear that if the bats are sold for $10\% $ loss then there will be a loss of Rs. 39.
Now in order to find the selling price of the 13 bats as per the given condition we have to subtract the loss amount from the cost price of the 13 bats i.e., we need to find the difference of 390 and 39.
And the difference of 390 and 39 i.e., 390-39 = 351.

Hence, the price of 13 bats when it is sold for $10\% $loss is Rs 351, So option D is correct.

Note:
Another approach to solve the question would be making use of formula $Loss = \dfrac{{Loss\% \times \operatorname{Cos} t\,price}}{{100}}$
Also, While simplifying equation $10 = \dfrac{{Loss}}{{390}} \times 100$ further we should first reduce 100 and 390 to its lowest terms instead of multiplying 390 to 10 and 100 to word Loss to avoid bigger number calculations that may increase the chance of getting wrong answer.