Question

The cost price of 30 boxes is the same as the selling price of x boxes. If the profit is 20%, the
value of x will be:
016
18
22
25​

Answer 1

Given :- The cost price of 30 boxes is the same as the selling price of x boxes. If the profit is 20%, the value of x will be :

A) 16

B) 18

C) 22

D) 25

Solution :-

given that,

→ CP of 30 boxes = Sp of x boxes .

So,

→ 30 CP = x SP

→ CP / SP = x / 30 .

now , given that, Profit is 20%..

So,

→ Profit = SP - CP

→ Profit = (30 - x)

Therefore,

→ Profit % = (Profit * 100) / CP

→ 20 = (30 - x) * 100 / x

→ 20x = (30 - x)100

→ 20x = 3000 - 100x

→ 20x + 100x = 3000

→ 120x = 3000

dividing by 40 both sides,

→ 3x = 75

dividing both sides by 3,

→ x = 25 . (Ans.) (option D).

Hence, CP of 30 boxes is equal to SP of 25 boxes when Profit is 20%.

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Answer 2

Given:

CP of 30 boxes = SP of x boxes

Profit Percentage= 20%

To Find:

The value of x

Solution:

$= > 30 \: CP \: = x \: SP$

$= > \dfrac{CP}{SP} = \dfrac{x}{30}$

$So, \: CP \: = x \: and \: SP = 30$

Profit:

$Profit \: = SP \: - \: CP$

$Profit \: = 30 - x$

Finding the value of x:

$Profit \% \: = \dfrac{Profit}{CP} \times 100$

$= > 20 = \dfrac{30 - x}{x} \times 100$

$= > (30 - x) \times 100 = 20x$

$= > 3000 - 100x = 20x$

$= > 100x + 20x = 3000$

$= > 120x = 3000$

$= > x = \dfrac{3000}{120}$

$= > x = 25$

$Hence, \: the \: value \: of \: x \: is \: 25$