Question

30. A craftsman is asked to manufacture three universal weights so that, using only these weights and a
simple balancing scale, it will be possible to measure any mass of consequtive integer number of
grams, starting from 1 gram, 2 grams, etc., up to a maximum possible mass of N grams. It is allowed
to place any of the three weights in any of the sides of the balancing scale, or to put any of them
aside. What is the greatest possible mass, N grams, that one can measure, given these requirements?
(A) 6 g
(B) 78
(C) 9g
(D) 10 g
(E) 13 g
5​

Answer 1

Given : three universal weights so that, using only these weights and a

simple balancing scale, it will be possible to measure any mass of consecutive integer number of grams, starting from 1 gram, 2 grams, etc., up to a maximum possible mass of N grams.

To Find : the greatest possible mass, N grams, that one can measure, given these requirements

Solution:

Three weights can be made up of

1 , 3 and 9 gram

1

3 - 1 = 2

3

3 + 1 = 4

9 - 3 - 1 = 5

9 - 3 = 6

9 + 1 - 3 = 7

9 - 1 = 8

9

9 + 1 = 10

9 + 3 - 1 = 11

9 + 3 = 12

9 + 3 + 1 = 13

Hence upto  13 g

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