A, B, C and D purchase a gift worth Rs.60. A pays \( \Large \frac{1}{2} \) of what others are paying, B pays \( \Large \frac{1}{3} \)rd of what others are paying and C pays \( \Large \frac{1}{4} \)th of what others are paying. What is the amount paid by D?

Let A, B, C and D pay Rs.x, Rs.y, Rs.z andrs.a

According to the question,

\( \Large x = \frac{1}{2} \left(y+z+a\right) \) ...(i)

\( \Large y = \frac{1}{3} \left(x+z+a\right) \) ...(ii)

\(  \Large z = \frac{1}{4} \left(x+y+a\right) \) ...(iii)

Also, x+ y+ z+a=60

Now, put the value of x + y + a = 4z

Then, 4z+ z = 60 => 52z = 60

Therefore, z = 12

Similarly, on putting the value of x + z + a = 3y, we get

3y + y = 60 => 4y = 60

Therefore, y = 15

Again, on putting the value of (y+ z+a) = 2x, we get

2x+ x=60 => 3x = 60

Therefore, x = 20

Now, x+ y+ z+a = 60

On putting the value of x,y and z, we get

12 + 15 + 20 + a = 60

Therefore, a = 60 - 47 = Rs.13