The cost price and the marked price of an item are ₹720 and ₹900 respectively. When it is sold at a discount of x%, the profit is $\frac{5 x}{3}$%, what is the value of x ?

$8 \frac{4}{7}$

CP = Rs. 720

MP = Rs. 900

According to the question,

900 × \(\frac{(100 - m) }{100}\)  = 720 × \(\frac{(300 +  5m) }{300}\)  

⇒ 900 × (100 - m) = 720 × \(\frac{(300 +  5m) }{3}\)  

⇒ 90000 – 900m = 240 × (300 + 5m)

⇒ 90000 – 900m = 72000 + 1200m

⇒ 2100m = 18000

⇒ m = \(\frac{18000}{2100}\)

⇒ m = \(\frac{60}{7}\)

⇒ m = $8 \frac{4}{7}$