NIMCET 2014 Question Paper with solutions

Let the weights of the five boxes, in increasing order be A, B, C, D and E. i.e. A < B < C < D < E.
Each of the boxes can be paired up with another box in a total of 4 ways.
If we sum up all the given weights, we get
4(A+ B+ C+ D+ E)= (110 + 112+113+114+115 + 116 + 117 + 118+120 + 121)
= 1156 kg
⇒ A + B + C + D + E = 289 kg ...(i)
Now, 121 kg is the sum of the weight of the boxes D and E and 110 is the sum of the weights of the boxes A and B. i.e. A+B = 110kg
and D + E = 121 kg
A + B + D + E= 231 kg ... (ii)
Subtracting Eq. (ii) from Eq. (i), we get
C =289-231 = 58 kg Now, 120 kg is the sum of the weights of the boxes C and E
i.e C+E = 120kg
⇒ E = (120 - 58) kg = 62 kg