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

Solution(By Examveda Team)

A + B + C + D = 60 -----------> (1)

Now According to Question,
A = $$\frac{1}{2}$$ (B + C + D)
2A = B + C + D
Put the value of B + C + D in Equation 1
A + 2A = 60
3A = 60
A = 20

Now again according to Question
B = $$\frac{1}{3}$$ (A + C + D)
A + C + D = 3B
By Putting the Value of A + C + D in Equation 1
we get,
B + 3B = 60
4B = 60
B = 15

Now again according to Question
C = $$\frac{1}{4}$$ (A + B + D)
A + B + D = 4C
By Putting the Value of A + B + D in equation 1
We get C + 4C = 60
5C = 60
C = 12

Since A + B + C + D = 60
20 + 15 + 12 + D = 60
D = 60 - 47 = 13
Amount of D = Rs. 13