A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment, while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has, B and D together also have the same number of cards as A and C taken together. If together they have 150 cards, how many cards has C got ?

Options

A. 28
B. 29
C. 31
D. 35

Answer

A

Explanation

According to the question
`A = B - 3 .....(i)`
`D+5 = E ....(ii)`
`A+ C = 2E ... (iii) `
`B + D = A + C = 2E ...(iv)`
`A+B + C + D + E = 150 ....(v)`
Using (iii) & (iv) in (v), we get
`2E + 2E + E = 150 [ because A+C=B+ D = 2E] `
or, `5E = 150 `
or, `E = 30 .....(vi)`
Putting the value of E from (vi) in (ii), we get
`D + 5 = 30 [because E = 30] `
or, `D = 25 `
Putting the values of E & D from (vi) & (vii) in (iv), we get
`B + 25 = 2 xx 30 [because E = 30, D = 25]`
or, `B= 60 -25 = 35 ... (viii) `
Putting the value of B from (viii) in (i), we get
`A = 35 - 3" " [because B = 35] `
or, `A= 32 `
Putting the value of A & E from (ix) & (vi) in (iii), we get
`32+ C = 2 xx 30 [because A= 32, E = 30] `
or, `C = 60 - 32 `
or, `C= 28 `
Therefore, Required number of cards with C= 28.