Question

(B+C) takes 50% time more than (A + B + C). If
all three takes Rs. 450 to complete a work then the
share of B is Rs. 120. In how many days will
(A+B+C) complete this work if (A + B) takes 8/3
days more than (A+B+C).​

Answer 1

If a, b, and c take x days

then b and c take 50% more days

means x + x/2 = 3x/2 days

ratio will be

a+b+c : b+c = x : 3x/2 = 2x : 3x

So ratio off efficiency becomes 3x : 2x

Now, efficiency of A is,

(A + B + C) - (B + C) = 3x - 2x

A = x

So, the efficiency of A is 1/3rd of (A+B+C) [i.e. 1/3 * 3x = x]

Now, share of B given 120 out of 450 = 120/450 = 4/15

We can find ratio of efficiencies now,

A = 1/3 = 5/15

B = 4/15

C = (15-4-5)/15 = 6/15

i.e. 5 : 4 : 6

Now, ratio of number of days = 1/5 : 1/4 : 1/6

=> 60x/5 : 60x/4 : 60x/6

=> 12x : 15x : 10x

Now, One day work of A & B = 1/12x + 1/15x = 9/60x

So, A & B will take 60x/9 days to complete the work.

therefore, A,B & C = 1/12x + 1/15x + 1/10x = 15/60x

So, A,B & C will take 60x/15 days to complete the work.

Now given that A and B take 8/3 days more than A, B and C

So, 60x/9 - 60x/15 = 8/3

Solving this we get x = 1

Thus number of days A, B and C will take to complete the whole work is 60x/15 = 4x = 4*1 = 4days.