A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how mar cards does B have ?

Options

A. 22
B. 23
C. 25
D. 35

Answer

C

Explanation

According to the question
`B-3=E .....(i)`
`B + 3 =D .....(ii)`
`A+B=D + E + 10 .... (iii) `
`B=C+2 .....(iv)`
`A + B + C + D + E = 133 ....(v)`
Adding (i) & (ii), we get
`2B = E +D `
Using (iii) & (iv), we get
`A+B= 2B + 10 [because E+ D = 2B] `
or, `A = B + 10 ... (vii) `
Using (iv), (vi) & (vii) in (v), we get
`(B + 10) + B + (B-2) + 2B = 133 `
`[because A=B+ 10, C=B-2, E+D=2B] `
or, `5B + 8 = 133 `
or, `5B = 133 - 8 `
or, `B = 125/5 = 25. `
Therefore, Required number of cards with B = 25.