Question

A toy was sold at a profit of 12%. If the cost price has been 10% less and selling price Re. 1 more, he would have made a profit of 25%. Find the cost price and the sell price to gain 20%.​



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Answer 1

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} \: }}:⟼

SP=

100

(100+Profit%)×CP

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}:⟼y=

100

(100+12)×x

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

100

(112)×x

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

y=

100

112x

−−−−(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} \: }}:⟼

SP=

100

(100+Profit%)×CP

we get now

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

100

112x

+1=

100

(100+25)

×

10

9x

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

100

112x+100

=

100

(125)

×

10

9x

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

2

9x

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

\rm :\longmapsto\:225x - 224x = 200:⟼225x−224x=200

\bf\implies \:x = 200⟹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} \: }}:⟼

SP=

100

(100+Profit%)×CP

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

100

(100+20)×200

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

1

120×2

\bf\implies \:SP = 200⟹SP=200

Hence,

Cost Price of radio = Rs 200

Selling Price of radio = Rs 240

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