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Melody

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यूजर का नामMelody
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Melody  11 Feb 2022
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jar:

A merchant bought some goods and set the selling price higher than the cost by 60%.
He sold 70% of them in the first month and the rest at a discount of x% in the second month.It is given that the overall profit was 37.5%.
(a)Find the value of x.
(b)Find the overall profit percentage if the rest of the goods are sold at a discount of 10%.


Hi jar,
WOW! That is one difficult question.
I'll talk you through part a and you can do part b by yourself.

To get my head around it I initially put some made up numbers in.
I said that 100 units were bought for $1 each. Making a total cost of $100
It doesn't matter what numbers you choose because the whole question is based on percentages.
anyway I solved it that way first, which is probably what you should do.
That answer will be correct and I also think that the method should be acceptable, especially if you point out your logic as I have done.
HOWEVER
I will show you a general solution anyway.

Original purchase
Q units are bought for $P each. Making the cost price PQ dollars

First months sales
70% of Q are sold for 60% profit
0.7Q sold for 1.6P
Total sales revenue for 1st month = 0.7Q * 1.6P = 1.12PQ

Second months sales
30% of Q are sold for ( 100% - x% ) of the first months price
30% of Q are sold for (1 - x/100 ) of 1.6P
0.3Q are sold for 1.6( 1- x/100 ) P
Total sales revenue for 2nd month = 0.3Q*1.6( 1- x/100)P => 0.48 ( 1 - x/100 )PQ

Total Revenue for the 2 months combined = 1.12PQ + 0.48(1 - x/100)PQ => [1.12+0.48(1 - x/100)]PQ

But you were told that the profit was 37.5% which means that
Total Revenue for the 2 months combined = 1.375 of PQ
so

[1.12+0.48(1 - x/100)]PQ = 1.375PQ

1.12+0.48(1 - x/100) = 1.375
and when you solve this you end up with
x = 46.875
that is
In the second month the price is discounted by 46.875%
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Questions like this should always be checked.
1.12PQ + 0.3Q*(1-0.46875)*1.6P => [1.12+0.48*0.53125]PQ => [1.12+0.255]PQ => 1.375PQ
That is, the total profit on cost price is 37.5%
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13 Jan 2014