# Twice the number of marbles in bag A is less than the number of marbles in bag B. The sum of the number of marbles in bags A and C is less than the number of marbles in bag B. There are more marbles in bag D than in bag B. There are 6 marbles in bag C and 9 marbles in bag D. How many marbles does bag B contain?

1
by RohitGupta866

2014-07-11T19:36:26+05:30
Twice the number of marbles in bag A is less than the number of marbles in bag B.
It implies 2A < B... (i)

The sum of the number of marbles in bags A and C is less than the number of marbles in bag B.
It implies A + C < B.... (ii)

There are more marbles in bag D than in bag B.
It implies B < D.... (iii)

There are 6 marbles in bag C and 9 marbles in bag D.
Therefore C = 6 & D = 9

Putting these values in (ii) & (iii)

Eq. (ii) A + 6 < B
Eq. (iii) B < 9

Now from eq. (iii) B = 8 , 7 , 6 , 5 ... 1
If B = 8 then ...
A + 6 < 8 ...
or, A + 6 = 7 , 6 ,...
As A + 6 can't take any values less than 7 as it will transform the value of A = 0 or less than 0, but the question satisfies it Bag A contains marbles....
Therefore A + 6 < 8 is true when A = 1...
Therefore our condition satisfies for B = 8.....
And 2A < B or, 2*1 < B or 2 < B or, 2 < 8 is also true...
Therefore the no. of marbles in bag B is 8