The weight of $X$, in kg, is denoted by $X$. The weights of $A$, $B$, $C$, $D$, $P$, $Q$, $R$ and $S$ are measured. Given : $$A + B + C + D = 17$$ $$A + C = 6$$ $$P + Q + S + D = 15$$ $$P + Q + R + B = 17$$ $$P = R ext{ and } Q = S$$
Which one of the following statements is correct?

Question

The weight of $X$, in kg, is denoted by $X$. The weights of $A$, $B$, $C$, $D$, $P$, $Q$, $R$ and $S$ are measured. Given : $$A + B + C + D = 17$$ $$A + C = 6$$ $$P + Q + S + D = 15$$ $$P + Q + R + B = 17$$ $$P = R 	ext{ and } Q = S$$
Which one of the following statements is correct?

Accepted Answer

$P$ and $Q$ together weigh more than the total weight of $A$ and $C$.

Explanation: From A + B + C + D = 17 and A + C = 6, we get B + D = 11. Using P = R and Q = S, equations (3) and (4) become: P + 2Q + D = 15 and 2P + Q + B = 17. Adding these: 3P + 3Q + (B + D) = 32. Substituting B + D = 11 gives 3(P + Q) = 21, so P + Q = 7. Since P + Q = 7 and A + C = 6, we have 7 > 6. Options 3 and 4 cannot be determined as individual values of P and Q are unknown. Therefore, P and Q together weigh more than A and C, making Option 2 the correct answer.

Detailed Explanation:

Question 2 of 3 Linear Equations

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