Question

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?

Answer 1

$$\begin{gathered} \mathrm{From}\mathrm{given}\mathrm{conditions} \\ \mathrm{B}=\mathrm{A}+3........\left(\mathrm{i}\right) \\ \mathrm{D}+5=\mathrm{E}........\left(\mathrm{ii}\right) \\ \mathrm{A}+\mathrm{C}=2\mathrm{E}........\left(\mathrm{iii}\right) \\ \mathrm{B}+\mathrm{D}=\mathrm{A}+\mathrm{C}........\left(\mathrm{iv}\right) \\ \mathrm{Also}\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}+\mathrm{E}=150 \\ \mathrm{from}\left(\mathrm{iii}\right)\&\left(\mathrm{iv}\right) \\ 2\mathrm{E}+2\mathrm{E}+\mathrm{E}=150 \\ \mathrm{E}=30 \\ \mathrm{from}\left(\mathrm{ii}\right) \\ \mathrm{D}=25 \\ \mathrm{from}\left(\mathrm{iv}\right) \\ \mathrm{B}+25=60 \\ \mathrm{B}=35 \\ \mathrm{from}\left(\mathrm{i}\right) \\ \mathrm{A}=35-3=32 \\ \mathrm{from}\left(\mathrm{iii}\right) \\ 32+\mathrm{C}=60 \\ \mathrm{C}=28\mathrm{Ans} \end{gathered}$$