Question

A tells B, “If you give e Rs 400 then I shall have 5/4 times as much as you have.” B tells A, “if you give me Rs 200, the I shall have three and half times as much as you have.” How much does B have

1) 1200
2) 900
3) 800
4) 1600​

Answer 1

Let money with A = x
Let money with B = y

x + 400/ y-400 = 5/4
4 ( x + 400 ) = 5 ( y - 400 )
4x - 5 y + 3600 = 0 ....(i)

(x -200)3.5 = y + 200
3.5x - y - 900 = 0
7x - 2y - 1800 = 0 ....(ii)

8x -10 y + 7200 = 0
35x -10y -9000 = 0
-27x + 16200 = 0
x = 16200/27 = 600

Putting x in equation (i)

2400 -5 y + 3600 = 0
y = 6000/5 = 1200

B has 1200

Answer 2

Option 1) 1200 is the correct answer.

Consider that,  money with A = x

                          money with B = y

Thus by the given conditions that “If you give  Rs 400 then I shall have 5/4 times as much as you have.”,

⇒    $\frac{x + 400}{y - 400} = \frac{5}{4}$

⇒ 4 ( x + 400 ) = 5 ( y - 400 )

⇒ 4x - 5 y + 3600 = 0  ........................................................................... (1)

Again it is given that, “if you give me Rs 200, then I shall have three and half times as much as you have.”

⇒  (x -200)3.5 = y + 200

⇒   3.5x - y - 900 = 0

⇒   7x - 2y - 1800 = 0 .................................................................................(2)

Multiplying (1) by 2 ⇒   8x -10 y + 7200 = 0 ............................................(3)

Multiplying (2) by 5 ⇒  35x -10y -9000 = 0 .............................................(4)

(3) - (4) ⇒  -27x + 16200 = 0

           ⇒                      x = $\frac{16200}{27}$

                                        = 600

Putting x in equation (1)

⇒ 4x 600 - 5 y + 3600 = 0

⇒     2400 -5 y + 3600 = 0

⇒                                y = $\frac{6000}{5}$

                                      = 1200

Thus, A has 600 and B has 1200.

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