Question

A told b "if you give me rs 400, then i shall have 25% more than what you have". b tells a, "if you give me rs 200, then i shall have three-and-a-half times as much as you have." how much does b have

Answer 1

Answer:   B has Rs. 1200.

Step-by-step explanation:  Given that A told B "if you give me Rs. 400, then i shall have 25% more than what you have".

B tells A, "if you give me Rs. 200, then i shall have three-and-a-half times as much as you have."

We are to find the amount of money that B has.

Let Rs. x and Rs. y represents the amount of money that A and B has respectively.

Then, according to the given information, we have

$x+400=(y-400)+25\%\times (y-200)\\\\\\\Rightarrow x+400=(y-400)+\dfrac{25}{100}\times(y-400)\\\\\\\Rightarrow x+400=(y-400)+\dfrac{y-400}{4}\\\\\\\Rightarrow x+400=\dfrac{5y-2000}{4}\\\\\Rightarrow 4x+1600=5y-2000\\\\\Rightarrow 4x=5y-3600\\\\\Rightarrow x=\dfrac{5y-3600}{4}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

and

$y+200=3\dfrac{1}{2}\times(x-200)\\\\\\\Rightarrow y+200=\dfrac{7}{2}(x-200)\\\\\\\Rightarrow 2y+400=7x-1400\\\\\\\Rightarrow 2y+400=7\times\dfrac{5y-3600}{4}-1400~~~~~~~~~~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\Rightarrow 8y+1600=35y-25200-5600\\\\\Rightarrow 8y+1600=35y-30800\\\\\Rightarrow 35y-8y=1600+30800\\\\\Rightarrow 27y=32400\\\\\Rightarrow y=\dfrac{32400}{27}\\\\\Rightarrow y=1200.$

Thus, B has Rs. 1200.