A man has certain notes of denominations ₹ 200 and ₹ 50 which amount to ₹ 3,800. If the number of notes of each kind is interchanged, they amount to ₹ 600 less as before. Find the number of notes of each denomination.

Let number of ₹ 200 notes be x and number of ₹ 50 notes be y.

So, total amount = 200x + 50y.

Given, total amount = ₹ 3,800.

∴ 200x + 50y = 3800 ………………..(1)

On exchanging number of notes, number of ₹ 200 notes will be y and number of ₹ 50 notes will be x.

Given, total amount in this case = 3200 (3800 - 600).

∴ 200y + 50x = 3200 ………………..(2)

Multiplying eq. (1) by 4 we get,

⇒ 4(200x + 50y) = 3800 x 4

⇒ 800x + 200y = 15200 ………………..(3)

Subtracting eq. (2) from (3) we get,

⇒ 800x + 200y - (200y + 50x) = 15200 - 3200

⇒ 800x - 50x + 200y - 200y = 12000

⇒ 750x = 12000

⇒ x = $\dfrac{12000}{750}$

⇒ x = 16.

Substituting the value of x in equation 1 we get,

⇒ 200(16) + 50y = 3800

⇒ 3200 + 50y = 3800

⇒ 50y = 3800 - 3200

⇒ 50y = 600

⇒ y = $\dfrac{600}{50}$

⇒ y = 12.

Hence, number of ₹ 200 notes = 16 and number of ₹ 50 notes = 12.