UPSC Prelims 2026 CSAT, question 8

Topic: Arithmetic

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 :

$A+B+C+D=17$

$A+C=6$

$P+Q+S+D=15$

$P+Q+R+B=17$

$P=R$ and $Q=S$

Which one of the following statements is correct?

(a) $B$ and $D$ together weigh less than the total weight of $P$ and $Q$ .
(b) $P$ and $Q$ together weigh more than the total weight of $A$ and $C$ .Correct answer
(c) $P$ weighs more than $Q$ .
(d) $Q$ weighs more than $P$ .

Solution.

Answer: (b) $P$ and $Q$ together weigh more than the total weight of $A$ and $C$ .

From $A + B + C + D = 17$ and $A + C = 6$ , we get $B + D = 17 - 6 = 11$ .
Adding $P + Q + S + D = 15$ and $P + Q + R + B = 17$ with $R = P$ and $S = Q$ gives $3(P + Q) + (B + D) = 32$ , so $3(P + Q) = 32 - 11 = 21$ and $P + Q = 7$ .
Since $P + Q = 7$ and $A + C = 6$ , $P$ and $Q$ together weigh more than the total weight of $A$ and $C$ .