A and B have some money with them. A said to B, 'if you give me ₹100, my money will become 75% of the money left with you'. "B said to A" instead if you give me ₹100, your money will become 40% of my money. How much money did A and B have originally?

Let A have ₹x and B have ₹y.

According to first condition,

$\Rightarrow x + 100 = \dfrac{75}{100}(y - 100)$

⇒ 100(x + 100) = 75(y - 100)

⇒ 100x + 10000 = 75y - 7500

⇒ 75y - 100x = 10000 + 7500

⇒ 75y - 100x = 17500

⇒ 25(3y - 4x) = 25 × 700

⇒ 3y - 4x = 700 …….(i)

According to second condition,

$\Rightarrow \dfrac{40}{100}(y + 100) = x - 100$

⇒ 40(y + 100) = 100(x - 100)

⇒ 40y + 4000 = 100x - 10000

⇒ 100x - 40y = 14000

⇒ 20(5x - 2y) = 20 × 700

⇒ 5x - 2y = 700 …….(ii)

Multiplying (i) by 2 and (ii) by 3 we get,

6y - 8x = 1400 ……(iii)

15x - 6y = 2100 …..(iv)

Adding (iii) and (iv) we get,

⇒ (6y - 8x) + (15x - 6y) = 1400 + 2100

⇒ 6y - 6y - 8x + 15x = 3500

⇒ 7x = 3500

⇒ x = 500.

Substituting value of x in (i) we get,

⇒ 3y - 4(500) = 700

⇒ 3y - 2000 = 700

⇒ 3y = 2700

⇒ y = 900.

Hence, A has ₹500 while B has ₹900.