A and B have 6 and 7 pieces of bread respectively. They share their food with C, who pays them Rs 42 for the received breads. If each of them has equal breads, provided that no bread is broken or wasted, find B’s share of the income from
C.

For breads to be equal, A+B = 6+7 = 13, which cannot be divided equally among three. Thus C has some bread initially. For, the breads to be equally distributable among the three, the total number of breads should be a multiple of 3, greater than 6+7 (13) = 15, 18, 21, 24…. If Total breads = 15, this means C had 2 breads initially Bread in each’s share = 5 This means A gave 1 and B gave 2 breads to C Now, suppose the total number of breads = 18 Breads initially with C = 18-13 = 5 This means each’s share is 6 bread each. For this to be the case, A should give nothing to C and B should give 1 bread to C to make all the three have equal breads but A has definitely shared some bread with C. Thus this case not possible. Thus, C initially had 2 breads and A gave 1 and B gave 2 breads to C. Now, money will be divided among A and B in the ratio 1:2 Rs. 42/3 = 14, B’s share = 14 x 2 = 28 Rs