Question

The cost price of 20 articles is the same as the cost price of x articles. If the profit is 25%, then the value of x is
[a] 15
[b] 16
[c] 18
[d] 25

Answer 1

Hint: Find the selling price in terms of cost prices using the formula for gain % age. Hence from the statement of the question form a linear equation in x. Solve for x. Alternatively, you can find the Selling price in terms of cost price and x and use the formula for gain % age form a linear equation in x and hence solve for x.

Complete step-by-step answer:

We have gain % age $=\dfrac{S.P-C.P}{C.P}\times 100$
$\dfrac{S.P-C.P}{C.P}\times 100=25$
Dividing both sides by 100, we get
$\dfrac{S.P-C.P}{C.P}=\dfrac{25}{100}$
Hence, we have $\dfrac{S.P-C.P}{C.P}=0.25$
Multiplying both sides by C.P, we get
S.P – C.P = 0.25C.P
Adding C.P on both sides, we get
S.P = 0.25C.P+C.P
i.e S.P = 1.25C.P.
Now, we know that S.P of x articles = C.P of 20 articles.
So, we have
$x\times S.P=20C.P$
Substituting S.P = 1.25 C.P, we get
$x\left( 1.25C.P \right)=20C.P$
Dividing both sides by C.P, we get
1.25x=20
Dividing both sides by 1.25, we get
$x=\dfrac{20}{1.25}=\dfrac{2000}{125}=16$
Hence the value of x is 16.
Hence option [b] is correct.

Note: Alternatively, we have
S.P of x articles = C.P of 20 articles.
So, we have $S.Px=20C.P$
Dividing both sides by xC.P, we get
$\dfrac{S.P}{C.P}=\dfrac{20}{x}$
We know that if $\dfrac{a}{b}=\dfrac{c}{d}$, then $\dfrac{a-b}{b}=\dfrac{c-d}{d}$
Using we get
$\dfrac{S.P-C.P}{C.P}=\dfrac{20-x}{x}$
But we know that gain % $=\dfrac{S.P-C.P}{C.P}\times 100$
Hence, we have $\dfrac{20-x}{x}=\dfrac{25}{100}$
Cross multiplying, we get
2000-100x =25x
Adding 100x on both sides, we get
125x =2000
i.e. x = 16
[2] If the value of x came to be fractional then there was no value of x for which the above condition can be met. This is because the number of articles is a Natural number and cannot be fractional.