Question

A and B have some money with them. B said to A if you give me ₹ 50, my money will be equal to your money. A said to B if you give me ₹ 100, my money will be equal to four times of your money. How much money did A and B have initially?

Answer 1

Given:

• A has some money say ₹ x.
• B has some money say ₹ y.
• B says: If A gives B ₹ 50, then B’s money will be equal to A’s money.
• A says: If B gives A ₹ 100, then A’s money will be four times B’s money.

Step-wise calculation:

1. From B’s statement: After A gives ₹ 50 to B:

• A will have x – 50.
• B will have y + 50.

According to B:

y + 50 = x – 50  

⇒ x – y = 100   ...(1)

2. From A's statement: After B gives ₹ 100 to A:

• A will have x + 100.
• B will have y – 100.

According to A:

x + 100 = 4(y – 100) 

⇒ x + 100 = 4y – 400

⇒ x – 4y = –500   ...(2)

3. Solve the system of equations (1) and (2):

From (1):

x = y + 100

Substitute into (2):

(y + 100) – 4y = –500 

y + 100 – 4y = –500 

–3y = –600 

y = 200

4. Substitute (y = 200) in (1): 

x – 200 = 100 

x = 300

A initially had ₹ 300.

B initially had ₹ 200.