Multiple choice

Passage

Directions: Read the following information and answer the given question. A doctor wanted to know the weight of 5 boys, each weighing less than 55 kg(Consider all the weights are natural numbers). The children would not let the doctor measure their weights on the weighing machine unless they were weighed in pairs. The weights (in kg) thus obtained were: 90, 92, 93, 94, 95, 96, 97, 98, 100 and 101. The names of the 5 children were Tinu, Minu, Chinu, Tipu and Tilu. Also, their weights were in the order Tilu > Tipu > Tinu > Minu > Chinu. The total weight of Tilu and Tipu is 101 kg, that of Minu and Chinu is 90 kg, and that of Tinu and Chinu is 92 kg.

What is the average weight of Tipu and Tinu?

  1. 48.1 kg

  2. 48.5 kg

  3. 49.5 kg

  4. 54.5 kg
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B Correct answer
Explanation

Let the weights be c < m < t < tp < tl. Given equations: m+c=90, t+c=92, tl+tp=101. Using the given sums and the ordering constraint, we can solve for individual weights. The average of Tipu and Tinu is (tp+t)/2 = 97/2 = 48.5.

AI explanation

Since the total weight of Minu and Chinu is 90 kg and Tinu and Chinu is 92 kg, we can determine the weight of Tipu. Adding the given weights of Tilu and Tipu (101 kg) to Minu and Chinu (90 kg) gives 191 kg, and adding Tinu and Chinu (92 kg) to Minu and Chinu (90 kg) gives 182 kg; subtracting the latter from the former means Tilu minus Tinu is 9 kg. The total sum of all pair weights is 956 kg, which equals four times the total weight of the five boys, so the total weight is 239 kg; subtracting Tilu and Tipu (101 kg) leaves the combined weight of Tinu, Minu, and Chinu as 138 kg. Subtracting the combined weight of Minu and Chinu (90 kg) from 138 kg gives Tinu's weight as 48 kg; subtracting Tilu's known total weight from the five boys means Tipu weighs 51 kg. Adding Tipu (51 kg) and Tinu (48 kg) gives 99 kg, and dividing by 2 results in an average weight of 48.5 kg.

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