# A and B Can Do a Work in 8 Days; B and C in 12 Days, and a and C in 16 Days. in What Time Could They Do It, All Working Together? - Mathematics

Sum

A and B can do a work in 8 days; B and C in 12 days, and A and C in 16 days. In what time could they do it, all working together?

#### Solution

A and B can do a work in = 8 days

B and C can do a work in = 12 days

A and C can do a work in = 16 days

(A+B)’s 1-day work =1/8

(B+C)’s 1-day work =1/12

(A+C)'s 1-day work =1/16

∴ [(A+B)+(B+C)+(A+C)]'s 1 day work

=1/8+1/12+1/16

i.e. [A+B+B+C+A+C]'s 1 day work

=1/8+1/12+1/16

=(6+4+3)/48=13/48

i.e. 2(A+B+C)'s 1-day work =13/48

i.e. (A+B+C)'s 1-day work =13/48xx1/2=13/96

∴ (A+B+C) can do the work in =96/13days

=7 5/13 days

Concept: Time and Work
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Chapter 10: Direct and Inverse Variations - Exercise 10 (E) [Page 133]

#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 10 Direct and Inverse Variations
Exercise 10 (E) | Q 12 | Page 133
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