Answer:
c) ₹ 24
Step-by-step explanation:
Find the cost price of 5 apples using the formula and then find the cost price of 12 apples.
Selling price (SP) of 5 apples = ₹14
Profit = 40%
To find the cost price (CP), we can use the formula,
[tex]\boxed{\bf CP =\dfrac{100 * SP}{100 + profit \%}}[/tex]
[tex]\sf = \dfrac{100 * 14}{100+40}\\\\\\=\dfrac{100*14}{140}\\\\\\[/tex]
CP = ₹10
CP of 5 apples = ₹10
CP of 1 apple = 10 ÷ 5
= ₹2
CP of 12 apples = 2*12
= ₹ 24
To find out how much the merchant paid for a dozen apples, we first determined the cost price for 5 apples by removing the included 40% profit from the selling price. Then, we calculated the cost for 10 and 2 apples separately and added them up to find the total cost for a dozen apples, which is Rs. 24. Option (C) is correct.
The student asked: How much did the merchant pay for a dozen apples if he sells them at the rate of 5 for Rs. 14, making a 40% profit?
First, let's find out the cost price (CP) for 5 apples by removing the profit. The selling price (SP) is given as Rs. 14 for 5 apples, and this includes a 40% profit on the CP. The profit is part of the SP:
SP = CP + Profit (Profit = 40% of CP)
Rs. 14 = CP + 0.40 × CP
Rs. 14 = 1.40 × CP
CP for 5 apples = Rs. 14 / 1.40
CP for 5 apples = Rs. 10
Now, let's calculate CP for a dozen (12) apples:
A dozen is 12, which is 5 apples × 2 + 2 extra apples. Since we have CP for 5 apples, let's compute for 12:
CP for 10 apples (5 × 2) = Rs. 10 × 2 = Rs. 20
CP for 2 apples is one-fifth of Rs. 10 as 5 apples cost Rs. 10:
CP for 2 apples = Rs. 10 / 5 × 2
CP for 2 apples = Rs. 4
CP for a dozen apples = Rs. 20 + Rs. 4 = Rs. 24
Therefore, the merchant paid Rs. 24 for a dozen apples.
