Question

A radio was sold at a profit of 12%. If the cost price had been 10% less and selling price Re. 1 more he would have made a profit of 25%. Find the cost price and selling price to gain 20%.? Ans-[200, 240]​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that,

↝ Cost Price of radio be Rs x.

And

↝ Selling Price of radio be Rs y.

Given that, A radio was sold at a profit of 12 %.

We know,

$\rm :\longmapsto\:\boxed{ \tt{ \: SP = \frac{(100 + Profit\%) \times CP}{100} \: }}$

where,

• SP is Selling Price of article

• CP is Cost Price of article.

So, on substituting the values, we get

$\rm :\longmapsto\:y = \dfrac{(100 + 12) \times x}{100}$

$\rm :\longmapsto\:y = \dfrac{(112) \times x}{100}$

$\rm \implies\:\boxed{ \tt{ \: y \: = \: \frac{112x}{100} \: }} - - - - (1)$

Now, Further given that

If the cost price had been 10% less and selling price Re. 1 more he would have made a profit of 25%.

So,

Cost Price of Radio = x - 10% of x = x - x/10 = 9x/10

Selling Price of radio = 112x/100 + 1

Profit % = 25 %

So, on substituting the values in the formula

$\rm :\longmapsto\:\boxed{ \tt{ \: SP = \frac{(100 + Profit\%) \times CP}{100} \: }}$

we get now

$\rm :\longmapsto\:\dfrac{112x}{100} + 1= \dfrac{(100 + 25)}{100} \times \dfrac{9x}{10}$

$\rm :\longmapsto\:\dfrac{112x + 100}{100} = \dfrac{(125)}{100} \times \dfrac{9x}{10}$

$\rm :\longmapsto\:112x + 100 = 25 \times \dfrac{9x}{2}$

$\rm :\longmapsto\:224x + 200 = 225x$

$\rm :\longmapsto\:225x - 224x = 200$

$\bf\implies \:x = 200$

Now, we have

Cost Price of radio = Rs 200

Profit % = 20 %

So,

$\rm :\longmapsto\:\boxed{ \tt{ \: SP = \frac{(100 + Profit\%) \times CP}{100} \: }}$

$\rm :\longmapsto\:SP = \dfrac{(100 + 20) \times 200}{100}$

$\rm :\longmapsto\:SP = \dfrac{120 \times 2}{1}$

$\bf\implies \:SP = 200$

Hence,

• Cost Price of radio = Rs 200

• Selling Price of radio = Rs 240

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$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{Gain = \sf S.P. \: – \: C.P.} \\ \\ \bigstar \:\bf{Loss = \sf C.P. \: – \: S.P.} \\ \\ \bigstar \: \bf{Gain \: \% = \sf \Bigg( \dfrac{Gain}{C.P.} \times 100 \Bigg)\%} \\ \\ \bigstar \: \bf{Loss \: \% = \sf \Bigg( \dfrac{Loss}{C.P.} \times 100 \Bigg )\%} \\ \\ \\ \bigstar \: \bf{S.P. = \sf\dfrac{100+Gain\% \: (or) \: 100 - Loss\%}{100} \times C.P.} \\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Given:

A radio was sold at a profit of 12%. If the cost price had been 10% less and selling price Re. 1 more he would have made a profit of 25%.

To Find:

Find the cost price and selling price to gain 20%?

Solution:

First, we are given that radio was sold at a profit of 12%, let the cost price of the radio be 100x, then the value of cost price and selling price will be,

CP=100x

SP=100x+12%

   =112x

Now it is said that if the cost price had been 10% less and selling price Re. 1 more he would have made a profit of 25%, then the value of cost price and selling price will be,

CP=100x-10%

   =90x

SP=112x+1

And it is also said that in this situation the profit% is 25%, so applying the formula for profit% we have,

$Profit\%=\frac{SP-CP}{CP} *100\\25=\frac{112x+1-90x}{90x}*100 \\5x=10\\x=2$

So we have the value of x as 2 then the value of cost price will be,

CP=100x

   =100*2

   =200

Now to get a profit of 20% the selling price would be,

SP=CP+20%

    =200+20%

    =200+40

    =240

Hence, the cost price is 200 and the selling price is 240 to gain 20%.