Question

By selling 40 greeting cards, a shopkeeper gains an amount equal to the selling price of five greeting cards. Find his gain percent.​

Answer 1

Answer:

100/7 %   or  14.28%

Step-by-step explanation:

Let the SP of 40 cards be x.  Given, gain is equal to selling price of 5 greeting cards.   ∴ Gain = (5/40) x = x/8 ,  if x is the SP.

Using gain = SP - CP

       ⇒ x/8 = x - CP

       ⇒ CP = x - x/8

       ⇒ CP = 7x/8

∴ Gain % = (gain)/CP * 100%

               = (x/8)/(7x/8) * 100%

               = 1/7 * 100%

               = 100/7  %

Answer 2

Given :

• By selling 40 greeting cards
• A shopkeeper gains an amount equal to the selling price of five greeting cards.

Solution :

Let assume that Selling price of 40 cards is K

Now, according to the question,

Gain = $\sf \frac{5}{40}×x = \frac{x}{8}$

if SP = x

We know that

Gain = SP - CP

Now , we have to put values in equation

Gain = SP - CP

$\sf \frac{x}{8} = x - CP$

$\sf CP = x - \frac{x}{8}$

$\sf CP = \frac{8x - x}{8}$

$\sf CP = \frac{7x}{8}$

Now as a question

Gain % = $\sf \frac{Gain}{CP} × 100 \%$

Gain % = $\sf \frac{\frac{x}{8}}{\frac{7x}{8}} × 100 \%$

Gain % = $\sf \frac{x}{8} × \frac{8}{7x} × 100 \%$

Gain % = $\sf \frac{\cancel{x}}{\cancel8} × \frac{\cancel8}{7\: \: \cancel{x}} × 100 \%$

Gain % = $\sf \frac{1}{7}× 100 \%$

Gain % = $\sf \underline{\underline{\frac{100}{7} \%}}$

Gain % = $\sf \underline{\underline {14.285 \% }}$

For more information

Here are a few formulas. Which will help you in SP, CP and gain's sums

1. Gain = (S.P.) - (C.P.)
2. Loss = (C.P.) - (S.P.)
3. Loss or gain is always reckoned on C.P.
4. Gain Percentage: (Gain %) Gain % = Gain x 100. C.P.
5. Loss Percentage: (Loss %) Loss % = Loss x 100. C.P.
6. Selling Price: (S.P.) SP = (100 + Gain %) x C.P. ...
7. Selling Price: (S.P.) SP = (100 - Loss %) x C.P. ...
8. Cost Price: (C.P.) C.P. = 100

I hope it helps you ❤️✔️

I have taken some little information from abhi569.