Question

A person purchase 90 clocks at sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20% had sold all the clocks at a uniform profit 15% his would have got Rs 40 less find the CP of each
clock

Answer 1

Given: A person purchase 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%.

To find: Cost price of each clock?

Solution:

• As we have given that he sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20% and he sold all the clocks at a uniform profit 15% his would have got Rs 40 ...........(i)

• So, let the cost price of each clock be x.

• So the cost price of the 90 clocks would be:

                90x.

• Now adding the prices with percentages from (i), we get:

                110% x 40x + 120% x 50x - 115%  x 90x = 40

• Solving further we get:

               (110/100 x 40x) + (120/100 x 50x) + (115/100 x 90x) = 40

                44x + 60x - 103.5x = 40

                x/2 = 40

                x = 80

Answer:

    So the cost price of each clock is 80 Rs.

Answer 2

Solution:

C.P => Cost price

S.P. => Selling Price

Let each clock C.P. be x

So , we can say that cost of 90 clocks will be 90x

He sells 40 clocks at a gain of 10% i.e. 110% and 50 clocks at a gain of 20% i.e. 120%

S.P. of 90 clocks = [(40x of 110%) + (50x of 120%)]

                            = $[(40x * \frac{110}{100} ) + (50x * \frac{120}{100})]$

                            = $[(4x * 11 ) + (5x * 12)]$

                            = $[44x + 60x]$

                            = $104x$

Now , he sold all the clocks at a uniform profit 15% i.e. 115% he would have got Rs 40 less.

S.P of 90 clocks(after uniform profit of 15% and also got 40 less) so,

104x - (90x of 115%) - 40 = 0

$104x - (90x * \frac{115}{100}) - 40 = 0$

$104x - \frac{1035x}{10} = 40$

$\frac{1040x - 1035x}{10} = 40$

$\frac{5x}{10}= 40$

$x = \frac{40 * 10}{5}$

$x = \frac{400}{5}$

$x = 80$

The C.P. of each clock is Rs. 80