a) ‘A’ ₹106, ‘B’ ₹198, ‘C’ ₹400 and ‘D’ ₹20

b) ‘A’ ₹98, ‘B’ ₹400, ‘C’ ₹20 and ‘D’ ₹106

c) ‘A’ ₹400, ‘B’ ₹20, ‘C’ ₹106 and ‘D’ ₹198

d) ‘A’ ₹98, ‘B’ ₹106, ‘C’ ₹20 and ‘D’ ₹400

correct answer is: d) ‘A’ ₹98, ‘B’ ₹106, ‘C’ ₹20 and ‘D’ ₹400

**Explanation**

Let think that A, B, C and D receive Rs a, b, c and d money respectively.

According to the question,

A receive 2 more = B receive 6 less = C receive 5 times = \frac{1}{4} of D receive.

Let assume that:

The new money receiving is ‘k’ . _{[here ‘k’ can be any number]}

So,

\rightarrow\ a + 2 = k

or, a = k -2

\rightarrow\ b - 6 = k

or, b = k + 6

\rightarrow\ 5c = k

or, c =\large \frac{k}{5}

\rightarrow\large \frac{d}{4}\normalsize = k

or, d = 4k

Therefore,

a + b + c + d = 624

\rightarrow\ (k\ -\ 2)\ +\ (k\ +\ 6)\ +\ \left(\frac{k}{5}\right)\ +\ 4k\ =\ 624

\rightarrow\large \frac{5k\ -\ 10\ +\ 5k\ +\ 30\ +\ k\ +\ 20k}{5}\normalsize = 624 _{[L.C.M = 5]}

\rightarrow\ 31k\ +\ 20\ =\ \left(624\ \times\ 5\right) _{[cross multiply]}

\rightarrow\ 31k + 20 = 3120

\rightarrow\ 31k = (3120 - 20)

\rightarrow\ 31k = 3100

\rightarrow\ k =\large \frac{3100}{31}

\rightarrow\ k = 100

So,

\therefore a = k - 2

\rightarrow\ a\ =\ \left(100\ -\ 2\right)\ = ₹98

\therefore b = k + 6

\rightarrow\ b\ =\ \left(100\ +\ 6\right)\ = ₹106

\therefore c =\large \frac{k}{5}

\rightarrow c =\large \frac{100}{5}\normalsize = ₹20

\therefore d = 4k

\rightarrow d = 4 \times 100 = ₹400

Ans: ‘A’ receives ₹98, ‘B’ receives ₹106, ‘C’ receives ₹20 and ‘D’ receives ₹400.

**Another variant of this particular question is:****1)** Find the distribution of ₹624 among A, B, C, and D, considering the specified conditions: A gets ₹2 more, B gets ₹6 less, C gets 5 times his share, and D gets 1/4th of his share.**2)** What are the individual shares of A, B, C, and D if ₹624 is divided among them, with A receiving ₹2 more, B receiving ₹6 less, C receiving 5 times his share, and D receiving 1/4th of his share?**3)** Solve the problem of dividing ₹624 among A, B, C, and D, where A gets ₹2 more, B gets ₹6 less, C gets 5 times his amount, and D gets 1/4th of his amount.**4)** Calculate the amounts each person A, B, C, and D receives if ₹624 is distributed among them, considering the given conditions.**5)** How to distribute ₹624 among four individuals A, B, C, and D given specific conditions on their shares?