Question

a alone can finish the work in 10 hours, b alone can finish the work in 12 hours and c alone can finish the work in 15 hours. a, b and c together started working at 11?o clock. after 2 hours a leaves. when will b & c will together will finish the work?

Answer 1

A alone can do it in = 10

B alone can do it in = 12

C alone can do it in = 15

Together they will do part work in 1 hour = 1/10 + 1/12 + 1/15

= (6+5+4) / 60 = 15/60 = 1/4

They worked for 2 hours, so = 1/4 * 2 = 1/2

Part of Work completed = 1/2

Part of work remaining = 1 - 1/2 = 1/2

1/2 work is completed by B and C together

Part of work done by B and C in 1 hour is,

= 1/12 + 1/15

= (5+4) / 60

= 9/60

= 3/20

B and C will finish whole work by working together in = 20/3 days

B and C will finish 1/2 work by working together in = 20/3 * 1/2

= 10/3 days

= 3 1/3 days.