# A Can Do a Piece of Work in 10 Days, B in 12 Days, and C in 15 Days. All Begin Together but a Leaves the Work After 2 Days and B Leaves 3 Days before the Work is Finished. How Long Did the Work Last? - Mathematics

Sum

A can do a piece of work in 10 days, B in 12 days, and C in 15 days. All begin together but A leaves the work after 2 days and B leaves 3 days before the work is finished. How long did the work last?

#### Solution

A's one day's work =1/10

B's one day's work =1/12

C's one day's work =1/15

A, B and C's one day's work =1/10+1/12+1/15

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

Let the work completed in x days

∴ A's 2 days work + B's (x − 3) days work + C's x days work = 1

⇒2xx1/10+("x"-3)xx1/12+"x"xx1/15=1

⇒1/5+("x"-3)/12+"x"/15=1

(12+5"x"-15+4"x"=60)/60 ...(L.C.M of 5, 12, 15 = 60)

⇒ 9x = 60 − 12 + 15

⇒ 9x = 63

⇒"x"=63/9=7

∴ Work will last for 7 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 15 | Page 133