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 with B. Who has the least amount of money ?

Options

A. B
B. C
C. D
D. Cannot be determined

Answer

A

Explanation

According to the given information:
`A+B=C+D." ....(i)"`
`B+D gt A+C." ....(ii)"`
`A gt B." ... (iii)"`
From (ii) & (iii), we get
`B+D gt A+C gt B+C " "[ because A gt B]`
or, `B+D gt B+C`
or, `D gt C." .....(iv)"`
From (i), (iii) & (iv), we get
`A+B=C+D`
Or, `2B lt A+B =C + D lt 2C" "[because A gt B and D gt C]`
or, `2B lt 2C`
or, `C gt B" ....(v)"`
From (iv) & (v), we get
`D gt C gt B" ... (vi)"`
Therefore, from (ii) & (vi) it is clear that B has the least amount.