A, B, C and D purchase a gift worth Rs. 60. A | vedclass

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Question

(D) Let the total amount be $A + B + C + D = 60$. Given: $A = \frac{1}{2}(B + C + D) \Rightarrow 2A = B + C + D$. Adding $A$ to both sides,$3A = A + B

Vedclass · Accepted Answer

$13$

Vedclass · Answer

(D) Let the total amount be $A + B + C + D = 60$. Given: $A = \frac{1}{2}(B + C + D) \Rightarrow 2A = B + C + D$. Adding $A$ to both sides,$3A = A + B + C + D = 60 \Rightarrow A = 20$. $B = \frac{1}{3}(A + C + D) \Rightarrow 3B = A + C + D$. Adding $B$ to both sides,$4B = A + B + C + D = 60 \Rightarrow B = 15$. $C = \frac{1}{4}(A + B + D) \Rightarrow 4C = A + B + D$. Adding $C$ to both sides,$5C = A + B + C + D = 60 \Rightarrow C = 12$. Now,$D = 60 - (A + B + C) = 60 - (20 + 15 + 12) = 60 - 47 = 13$. Thus,the amount paid by $D$ is $Rs. 13$.

$A, B, C$ 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 $D$?

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