Question

Nehalem sold her old bicycle suffering a loss of 6%.If she had sold her bicycle for rupees 90more,she would have made a profit of 3%. Find the cost price of the bicycle?

Answer 1

$\rm\red{\underbrace{Answer\implies Rs.1000}}$

$\sf\large\underline{Let:}$

$\tt{\implies The\:cost\:_{(bicycle)}=x}$

$\sf\large\underline{To\: Find:}$

$\tt{\implies The\:cost\:_{(bicycle)}=?}$

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

• To calculate the cost price of bicycle we have to use formula. By applying it we will find out the cost price of bicycle here]

$\sf\large\underline{Formula\:used:}$

$\tt{\implies SP=\bigg(\dfrac{100-L\%}{100}\bigg)\times\:CP}$

$\sf\small\underline{Given\:in\:1st\:case:}$

• Nehalem sold her old bicycle suffering a loss of 6%]

$\tt{\implies SP=\bigg(\dfrac{100-6}{100}\bigg)\times\:6}$

$\tt{\implies SP=\dfrac{94x}{100}}$

• Here she sold the bicycle Rs.90 more

$\tt{\implies SP=\dfrac{94x}{100}+90----(i)}$

$\sf\small\underline{Given\:in\:2nd\:case:}$

• she would have made a profit of 3%.]

$\tt{\implies SP=\bigg(\dfrac{100+G\%}{100}\bigg)\times\:CP}$

$\tt{\implies SP=\bigg(\dfrac{100+3}{100}\bigg)\times\:x}$

$\tt{\implies SP=\dfrac{103x}{100}----(ii)}$

• Now calculate the cost price of bicycle here]

$\tt{\implies SP\:_{(ii)}=SP\:_{(i)}}$

$\tt{\implies \dfrac{103x}{100}=\dfrac{94x}{100}+90}$

$\tt{\implies \dfrac{103x}{100}-\dfrac{94x}{100}=90}$

$\tt{\implies \dfrac{103x-94x}{100}=90}$

$\tt{\implies \dfrac{9x}{100}=90}$

$\tt{\implies 9x=9000\implies x=1000}$

$\sf\large{Hence,}$

$\tt{\implies The\:cost\:_{(bicycle)}=Rs.1000}$