Prakash sells ready-made shirts. He purchased 160 shirts from a company outlet at rs.x per shirt. If he sells 20% of the shirts at 15% profit and 37.5% of the remaining shirts at 40% profit, at what profit percentage should he sell the remaining to make a profit of 25% on the whole?

Hello Ritika,

The question is really tricky but can be solved by applying the basics clearly.

So, as per the question, the cost price of one shirt is rs. x

therefore, cost price of 160 shirts = 160 x

As per the last condition, the overall profit is of 25%.

So, Overall Selling price = 160 x + ( 25% of 160 x )

So, overall selling price = 200 x....................( a )

Now, 20 % of total shirts are sold at a profit of 15%

20% of total shirts = 20% of 160 = 32 shirts.

So, Selling Price ( i ) = 32 x + ( 15 % of 32 x )

So, Selling Price ( i ) = 36.8 x..................... ( 1 )

Now, 37.5% of remaining shirts are sold at 40% profit.

So, 37.5% of remaining shirts = 37.5% of ( 160-32 ) = 48

So, Selling price ( ii ) = 48 x + ( 40% of 48 x )

So, Selling price ( ii ) = 67.2 x....................( 2 )

Now, let the remaining shirts are sold for y% profit.

Remaining shirts = 160 - 32 - 48 = 80

So, Selling price ( iii ) = 80 x + ( y% of 80 x )............ ( 3 )

Now, ( 1 ) + ( 2 ) + ( 3 ) = ( a )

So, 36.8 x + 67.2 x + [ 80 x + ( y% of 80 x ) ] = 200 x

Solving for y, we get y = 20%.

So, the remaining shirts will need to be sold at 20% profit.

Best Wishes.

Let x be 100
Now 20% of 160 is 32
Then he sells 32 shirts at 15% profit i.e 115rs per shirt .
Now 128 shirts are remaining.
37.5%of 128 is 48.
He sells this 48 shirts at 40% profit that is
140 rs per shirt.
Hence the actual total price is 16000
And now money earned is 115*32+140*48=10400.
80 shirts are remaining.
If he wants to make 25% profit as a whole then the total money earned should be 160*125=20000
Hence 80 shirts total selling price have to be 9600.
Hence 120rs per shirt.
So he has to make 20% profit