Question

The cost price of a bat and ball is rs.75.the retailer sold bat at 40% profit and ball at 60% loss.find the cost price of the bat if in the whole transaction he earns rs.20 as profit?

Answer 1

Given :

The total cost price of bat and ball = Rs 75

The profit% on bat = 40 %

The loss% on ball = 60%

Profit earn on whole transition = Rs 20

To Find :

The cost price of the bat

Solution :

Let The cost price of bat = Rs A

Let The cost price of ball = Rs B

∵ total cost price of bat and ball = Rs 75

So,   A   +   B =  Rs 75

Again

Profit% for bat = $\dfrac{S.P_1- C.P_1}{C.P_1}$

Or,  40% = $\dfrac{S.P_1- C.P_1}{C.P_1}$

or,   $\dfrac{40}{100}$ = $\dfrac{S.P_1- C.P_1}{C.P_1}$

Or, $\dfrac{40}{100}$  + 1 = $\dfrac{S.P_1}{C.P_1}$

i.e  $\dfrac{S.P_1}{C.P_1}$ = 1.4

$S.P_1 = 1.4 C.P_1$

Again

Loss% for ball = $\dfrac{C.P_2- S.P_2}{C.P_2}$

Or, 60% = $\dfrac{C.P_2- S.P_2}{C.P_2}$

Or,  $\dfrac{60}{100}$ = $\dfrac{C.P_2- S.P_2}{C.P_2}$

Or,  $\dfrac{S.P_2}{C.P_2}$ = 1 - $\dfrac{60}{100}$

i.e  $\dfrac{S.P_2}{C.P_2}$ = 0.4

Or,  $S.P_2= 0.4 C.P_2$

A/Q

Total cost price of bat and ball = Rs 75

i.e $C.P_1$ + $C.P_2$ = 75       .............1

∵  Total profit = Rs 20

Or,  [ ( $S.P_1 - C.P_1$ ) + ( $S.P_2 - C.P_2$ ) = 20

Or,  [ $S.P_1 + S.P_2$ ) - ( $C.P_1 + C.P_2$ )] = 20

Or,  $S.P_1 + S.P_2$ = 20 + $C.P_1 + C.P_2$

∴    $S.P_1 + S.P_2$ = 20 + 75

i.e  $S.P_1 + S.P_2$ = Rs 95

As $S.P_1$  = 1.4 $C.P_1$

And  $S.P_2$  = 0.4 $C.P_2$

So,  1. 4 $C.P_1$  +  0.4 $C.P_2$  = 95       ..........2

Solving eq 1 and eq 2

 ( 1.4 $C.P_1$  +  0.4 $C.P_2$  ) - 0.4 ( $C.P_1$ + $C.P_2$ ) = 95 - 0.4 × 75

i.e  1 $C.P_1$ + 0  = 95 - 30

Or,   $C.P_1$  = 65

∴    $C.P_1$  = $\dfrac{65}$

i,e  $C.P_1$ = Rs 65

So,The cost price of bat = $C.P_1$ = Rs 65

Hence, The cost price of bat in whole transition is Rs 65 Answer