# A and B Complete a Piece of Work in 24 Days. B and C Do the Same Work in 36 Days; and A, B, and C Together Finish It in 18 Days. in How Many Days Will: (I) a Alone, (Ii) C Alone - Mathematics

Sum

A and B complete a piece of work in 24 days. B and C do the same work in 36 days; and A, B, and C together finish it in 18 days. In how many days will:
(i) A alone,
(ii) C alone,
(iii) A and C together, complete the work?

#### Solution

A and B complete a piece of work in = 24 days

B and C complete a piece of work in = 36 days

(A+B+C) complete a piece of work in = 18 days

(A+B)’s 1-day work = 1/24

(B+C)’s 1-day work = 1/36

(A+B+C)’s 1-day work = 1/18

(i) A's 1-day work =1/18-1/36

=(2-1)/36=1/36

∴ A will complete the work in = 36 days

(ii) C's 1-day work =1/18-1/24

=(4-3)/72=1/72

∴ C will complete the work in = 72 days

(iii) (A+C)'s 1-day work =1/36+1/72

=(2+1)/72=3/72

=1/24

∴ (A+C) will complete the work in = 24 days

Concept: Time and Work
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#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 10 Direct and Inverse Variations
Exercise 10 (E) | Q 13 | Page 133