There are four persons A, B, C and D. The total amount of money with A and B together is equal to the total amount of money with C and D together. But the total amount of money with B and D together is more than the amount of money with A and C together. The amount of money with A is more than that B. Who has the least amount of money?
I tried to solve this question, not once but many times and also searched on the internet. It is question from a verbal reasoning (puzzle test)?
$A+C=C+D$ implies $A=D$. Then $A+B=D+B>A+C$ implies $B>C$. As we are also given that $A>B$, we fined $$D=A>B>C$$ and $C$ is the poorest.
From the given conditions: $$ A + C = C + D \Rightarrow A = D$$ $$ B + D > A + C \Rightarrow B + A > C + A \Rightarrow B > C$$ $$ A > B $$ So we have, $$ A = D > B > C $$
We have $A+B=C+D\cdots\cdots(1)\\B+D>A+C\cdots\cdots(2)\\A>B\cdots\cdots(3)$
From $(3)$ we get that $D>C.$
Adding $B$ on both sides of $(1)$.
$A+2B=C+D+B.\\or,\,A+2B-C=B+D>A+C.\space \space [\text {Using (2)}]\\or,\,A+2B-C>A+C.\\or,\,2B>2C.\\or,\,B>C.$
So $C$ has the least amount of money.
If $ A>D$ ,
$A+B=C+D\\\implies A+B-C=D\\\implies A+B-C<A\\\implies B-C<0\\\implies B<C. $
