A man bought a certain number of oranges; out of which 13 percent were found rotten. He gave 75% of the remaining in charity and still had 522 oranges left. Find how many oranges had he bought ?

Let the number of oranges the man bought be $x$.

Percentage of rotten oranges = 13%

Percentage of remaining oranges = (100% - 13%) = 87%

No. of remaining oranges = 87% of x

= $\dfrac{87}{100} \times x$

= $\dfrac{87x}{100}$ ……………(1)

Oranges given to charity = 75% of the remaining oranges.

Left over oranges = (100% - 75%) = 25% of the remaining oranges = 522

From equation (1), we get

⇒ 25% of $\dfrac{87x}{100}$ = 522

⇒ $\dfrac{25}{100} \times \dfrac{87x}{100} = 522$

⇒ $\dfrac{1}{4} \times \dfrac{87x}{100} = 522$

⇒ $\dfrac{1 \times 87x}{4 \times 100} = 522$

⇒ $\dfrac{87x}{400} = 522$

⇒ $x = \dfrac{522 \times 400}{87}$

⇒ $x = \dfrac{2,08,800}{87}$

⇒ $x = 2,400$

Hence, the total number of oranges = 2,400.