Question

Instead of dividing rupees. 180 among a, b, c in the ratio (1/3):(1/4):(1/6) respectively, it was divided in the ratio rs. 3:4:6 by mistake. Who gain in transaction.

Answer 1

180 was divided in 3:4:6 among a,b and c

So A's share = 180 * 3/13 = 540/13 = 41.54

B's share = 180 * 4/13 = 720/13 = 55.38

C's share = 180 * 6/13 = 1080/13 = 83.08

180 should have been divided in ratio (1/3):(1/4):(1/6)

Taking LCM of denominators 3,4 and 6 = 12

1/3 = 4/12

1/4 = 3/12

1/6 = 2/12

Now Ratio is 4/12 : 3/12 : 2/12 which is 4:3:2

Dividing 180 in 4:3:2

A's share = 180 * 4/9 = 80

B's share = 180 * 3/9 = 60

C's share = 180 * 2/9 = 40

So A got 41.54 instead of 80, Loss of 38.46

B got 55.38 instead of 60, Loss of 4.72

C got 83.08 instead of 40, Gain of 43.08

So, C gained in this transaction.

Answer 2

180 was divided in 3:4:6

among a,b and c

So share of A= 180 * 3/13 = 540/13 = 41.54

share of B= 180 * 4/13 = 720/13 = 55.38

share of c = 180 * 6/13 = 1080/13 = 83.08

180 should has been divided in ratio

(1/3):(1/4):(1/6)

LCM of denominators 3,4 and 6 = 12

1/3 = 4/12

1/4 = 3/12

1/6 = 2/12

Now Ratio is

4/12 : 3/12 : 2/12

which is 4:3:2

Divide

180 in 4:3:2

share of A = 180 * 4/9 = 80

share of B= 180 * 3/9 = 60

share of C = 180 * 2/9 = 40

So A got 41.54 instead of 80

loss of A=80-41.54=38.46

B got 55.38 instead of 60,

Loss of B=60-55.38=4.72

C got 83.08 instead of 40,

Gain of c=83.08-40= 43.08

So, C gained in this transaction