Question

If Fatima sells 60 identical toys at a 40% discount on the printed price, then she makes 20% profit. Ten of these toys are destroyed in fire. While selling the rest, how much discount should be given on the printed price so that she can make the same amount of profit?

Answer 1

The discount that should be given on the printed price so that Fatima can make the same amount of profit is 28%.  

Step-by-step explanation:

Step 1:

No. of toys Fatima sells at 40% discount = 60

Profit % = 20%

Let’s assume the printed price of the toys i.e., the marked price be “M.P.” and the cost price of the toys be “C.P.”.

So, we can write the eq. as,

$\frac{[60*(M.P.-0.40M.P.)] - [60C.P.]}{60C.P.} *100 = 20$ …… [since Profit% = $\frac{S.P. - C.P.}{C.P.} * 100$]

⇒ [{36 M.P. – 60 C.P.} / {60 C.P.}] = 0.2

⇒ 36 M.P. = 60 C.P. + 12 C.P.

⇒ 36 M.P. = 72 C.P.

⇒ M.P. = 2 * C.P.

Step 2:

Now, it is given that 10 toys are burnt in fire, so we are left with (60-10=) 50 toys and also we need to give discount in such a way so that the profit remains the same as 20 %.

Let the required discount be denoted as “x”%.

Similarly as above, we can write the eq. as,

$\frac{[50*(M.P.- xM.P.)] - [60C.P.]}{60C.P.} *100 = 20$

substituting M.P. = 2 * C.P.

⇒$\frac{[50*2*C.P. *(1 - x)] - [60C.P.]}{60C.P.} *100 = 20$

⇒ 100 C.P. – 100xC.P. – 60C.P. = 12 C.P.

⇒ 40 C.P. – 100xC.P. = 12 C.P.

⇒ 100x * C.P. = 28 * C.P.

⇒ x = $\frac{28}{100}$

⇒ x = 28%

Thus, a discount of 28% should be given on the printed price so that Fatima can make the same amount of profit while selling the rest of the toys.

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