Ram, Shyam,Tarun and Varun together had a total amount of Rs. 240 with them. Ram had half of the total amount with the others.

Correct option is (C) 52

Let Ram, Shyam, Tarun and Varun had amount of Rs x, y, z and w respectively.

\(\because\) They had a total amount of Rs 240 together.

\(\therefore\) x+y+z+w = 240        ______________(1)

According to other given conditions, we have

\(x=\frac{y+z+w}2\)

\(\Rightarrow\) y+z+w = 2x        ______________(2)

\(y=\frac{x+z+w}3\)

\(\Rightarrow\) x+z+w = 3y        ______________(3)

and \(z=\frac{x+y+w}4\)

\(\Rightarrow\) x+y+w = 4z        ______________(4)

From (1) & (2), we obtain

x+2x = 240

\(\Rightarrow\) 3x = 240

\(\Rightarrow\) x = 80

From (1) & (3), we obtain

y+3y = 240

\(\Rightarrow\) 4y = 240

\(\Rightarrow\) y = 60

From (1) & (4), we obtain

z+4z = 240

\(\Rightarrow\) 5z = 240

\(\Rightarrow\) z = \(\frac{240}5\) = 48

Put x = 80, y = 60, z = 48 in (1), we get

80+60+48+w = 240

\(\Rightarrow\) w = 240 - 188

= 52

Hence, the amount which Varun has Rs 52.