Problems on Simultaneous Linear Equations | Problems on Simultaneous Linear Equations Exercise 6

Question

A and B have some money with them. A said to B, “if you give me Rs. 100, my money will

become 75% of the money left with you.” B said to A” instead if you give me Rs. 100, your money

will become 40% of my money. How much money did A and B have originally?

Accepted Answer

Let’s assume A has money = x

And B has money = y

Then according to the given conditions, we have

x – 100 = (y - 100) x (75/100)

x – 100 = (y - 100) x (3/4)

4x – 400 = 3y – 300

4x – 3y = 400 – 300

4x – 3y = 100 … (i)

Also,

x – 100 = (y + 100) (40/100)

x – 100 = (y + 100) (2/5)

5x – 500 = 2y + 200

5x – 2y = 200 + 500

5x – 2y = 700 … (ii)

Now, multiplying (i) by 2 and (ii) by 3, we have

8x – 6y = -1400

15x – 6y = 2100

(-)—(+)---(-)----

-7x = -3500

x = -3500/ -7

x = 500

On substituting the value of x in (i), we get

4(500) – 3y = -700

2000 – 3y = -700

3y = 2000 + 700

y = 2700/3

y = 900

Therefore, A has money Rs 500 and B has money Rs 900.

Question 32