Question

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

Answer 1

SOLUTION :
Let A has money = ₹ x & B has money =₹ y
ATQ :
1st case :
(x+100) = 75%(y-100)
(x+100) = 75/100(y-100)
(x+100) = 3/4(y-100)
4 (x+100) = 3(y-100)
4x + 400 = 3y - 300
4x - 3y = - 300 - 400
4x - 3y = - 700 ……………..(1)

2nd case:
(x-100) = 40% (y+100)
(x-100) = 40/100 (y+100)
(x-100) = 2/5 (y+100)
5 (x-100) = 2 (y+100)
5x - 500 = 2y + 200
5x - 2y = 200 + 500
5x - 2y = 700…………….(2)

Multiply eq 1 by 5 & eq 2 by 4 and On subtracting eq ( 4 ) from ( 3)

20 x - 15 y = - 3500 …………..(3)
20 x - 8 y = 2800 ……………(4)
(-)     (+)     (-)
----------------------
- 7 y = - 6300
7 y = 6300
y = 6300/7 = 900
y = 900

On putting the value of y in eq ( 4) 
20 x - 8 y = 2800
20 x - 8(900) = 2800
20 x - 7200 = 2800
20 x = 2800 + 7200
20 x = 10000
x = 10000/20
x = 500

Hence, A has money = ₹ 500 and B has money =₹ 900

HOPE THIS WILL HELP YOU...

Answer 2

Let a has x rupees and b has y rupees
So, as per the conditions
(x+100)=75/100  (y-100)
4(x+100)=3(y-100)
4x+400 = 3y- 300
4x-3y= -700..........1

As per 2nd condition,
(x-100)=40/100  (y+100)
5(x-100)= 2(y+100)
5x-500=2y+200
5x-2y = 700 ..............2

Adding equation 1 and 2
9x- 5y =0
9x = 5y
y=(9x)/5
Substituing this value in equation 2
5x - (18x)/5 = 700
(25x - 18x)/ 5 = 700
(7x) / 5 = 700
x=(700 × 5)/7
x=500
Now, y= (9x/5)
y= (9 ×500)/5
y= 900

So, A has 500 rupees and B has 900 rupees