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Quantitative Reasoning – All possible weights!

PSA 2014_XI_Q2. Four small boys want to know their weights, but the weighing machine only weighs objects more than 40 kg. As each of the boys knows that his weight is less than this, they weigh themselves two at a time. The results of all possible paired weighings are: 48 kg, 49 kg, 52 kg, 53 kg, 56 kg and 57 kg.
Mohinda, the tallest of the four boys, weighs the most.
What does he weight?
1) 29 kg
2) 30 kg
3) 31 kg
4) 32 kg

Let the weight of the four boys in increasing weights be W1, W2, W3 & W4.

W1 + W2= 48 –(A)
W1 + W3= 49 –(B)
W1+ W4= 52 –(C)
W2+ W3= 53 –(D)
W2+ W4= 56 –(E)
W3+ W4= 57 –(F)

From (B)-(A), W3-W2 = 1 –(G)

From (G) + (D), 2W3=54

Therefore, W3= 27. Substituting the values of W3, we get

W1=22; W2=26; W4=30. Option (2).

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