Four small boys want to know their weights,but the weighing machine only weighs object more than 40kg As each of - PSA - Quantitative Reasoning

Question

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

Koka Sri Lakshmi Divya Sai · Accepted Answer

Let the weight of four boys be w1,w2,w3, and w4kg∴If,we
select two different boys from the four,we can do it in C24wayswe
have six different weights given to usw1+w2=48kg w1+w3=49kg
w1+w4=52kg w2+w3=53kgw4+w2=56kg
w3+w4=57kg∴w1+w2+w3+w4=105kgw1+w4+w2+w4+w3+w4=52+56+57=165kg⇒(w1+w2+w3+w4)+2w4=165kg⇒w4=165-1052=30kgw3=27kg,
w2=22kg and w1=26kg∴Weight of Mohinda=30kg