13. Ram had some money. He gave \( \frac{2}{5} \) of it to his son, \( \frac{3}{8} \) of it to his daughter and the remaining amount to his wife. If the wife gets \( ₹ 18,000 \), what was the total amount?

Let's denote the total amount of money Ram had as \( x \). According to the problem, he gave: - \( \frac{2}{5}x \) to his son, - \( \frac{3}{8}x \) to his daughter. The remaining amount given to his wife is represented as: \[ x - \left(\frac{2}{5}x + \frac{3}{8}x\right) = ₹ 18,000. \] To solve for \( x \), we start by finding a common denominator for \( \frac{2}{5} \) and \( \frac{3}{8} \). The least common multiple of 5 and 8 is 40. Rewriting the fractions: \[ \frac{2}{5} = \frac{16}{40}, \quad \frac{3}{8} = \frac{15}{40}. \] Adding these fractions: \[ \frac{2}{5}x + \frac{3}{8}x = \left(\frac{16}{40} + \frac{15}{40}\right)x = \frac{31}{40}x. \] Now substituting this back into the remaining amount: \[ x - \frac{31}{40}x = ₹ 18,000, \] This simplifies to: \[ \frac{9}{40}x = ₹ 18,000. \] To find \( x \): \[ x = ₹ 18,000 \times \frac{40}{9} = ₹ 80,000. \] Thus, the total amount Ram had is \( ₹ 80,000 \).