Question and Answers Forum

All Questions      Topic List

UNKNOWN Questions

Previous in All Question      Next in All Question      

Previous in UNKNOWN      Next in UNKNOWN      

Question Number 9167 by nazar last updated on 21/Nov/16

A can do a work in 10 days and B can  do the same work in 15 days. How   many days will they take if  both work  together?

$$\mathrm{A}\:\mathrm{can}\:\mathrm{do}\:\mathrm{a}\:\mathrm{work}\:\mathrm{in}\:\mathrm{10}\:\mathrm{days}\:\mathrm{and}\:\mathrm{B}\:\mathrm{can} \\ $$$$\mathrm{do}\:\mathrm{the}\:\mathrm{same}\:\mathrm{work}\:\mathrm{in}\:\mathrm{15}\:\mathrm{days}.\:\mathrm{How}\: \\ $$$$\mathrm{many}\:\mathrm{days}\:\mathrm{will}\:\mathrm{they}\:\mathrm{take}\:\mathrm{if}\:\:\mathrm{both}\:\mathrm{work} \\ $$$$\mathrm{together}? \\ $$

Commented by tawakalitu last updated on 22/Nov/16

Let the time it take both of them be = x  ∴  x((1/(10)) + (1/(15))) = 1  ∴  x(((15 + 10)/(150))) = 1  ∴  x(((25)/(150))) = 1  ∴  x((1/6)) = 1  ∴  (x/6) = 1  Cross multiply  ∴  x = 6  Hence it will take both of them 6 days to   finish the work if they both work together.  DONE !

$$\mathrm{Let}\:\mathrm{the}\:\mathrm{time}\:\mathrm{it}\:\mathrm{take}\:\mathrm{both}\:\mathrm{of}\:\mathrm{them}\:\mathrm{be}\:=\:\mathrm{x} \\ $$$$\therefore\:\:\mathrm{x}\left(\frac{\mathrm{1}}{\mathrm{10}}\:+\:\frac{\mathrm{1}}{\mathrm{15}}\right)\:=\:\mathrm{1} \\ $$$$\therefore\:\:\mathrm{x}\left(\frac{\mathrm{15}\:+\:\mathrm{10}}{\mathrm{150}}\right)\:=\:\mathrm{1} \\ $$$$\therefore\:\:\mathrm{x}\left(\frac{\mathrm{25}}{\mathrm{150}}\right)\:=\:\mathrm{1} \\ $$$$\therefore\:\:\mathrm{x}\left(\frac{\mathrm{1}}{\mathrm{6}}\right)\:=\:\mathrm{1} \\ $$$$\therefore\:\:\frac{\mathrm{x}}{\mathrm{6}}\:=\:\mathrm{1} \\ $$$$\mathrm{Cross}\:\mathrm{multiply} \\ $$$$\therefore\:\:\mathrm{x}\:=\:\mathrm{6} \\ $$$$\mathrm{Hence}\:\mathrm{it}\:\mathrm{will}\:\mathrm{take}\:\mathrm{both}\:\mathrm{of}\:\mathrm{them}\:\mathrm{6}\:\mathrm{days}\:\mathrm{to}\: \\ $$$$\mathrm{finish}\:\mathrm{the}\:\mathrm{work}\:\mathrm{if}\:\mathrm{they}\:\mathrm{both}\:\mathrm{work}\:\mathrm{together}. \\ $$$$\mathrm{DONE}\:! \\ $$

Commented by mrW last updated on 22/Nov/16

The solution can be generalized  as following:

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{can}\:\mathrm{be}\:\mathrm{generalized} \\ $$$$\mathrm{as}\:\mathrm{following}: \\ $$

Commented by mrW last updated on 22/Nov/16

Commented by sandy_suhendra last updated on 22/Nov/16

it can be solved by this way :  in 1 day A can do = (1/(10)) part of work  in 1 day B can do = (1/(15)) part of work  in 1 day A and B can do = (1/(10))+(1/(15))=(1/6) part of work  so A and B can do the work in 6 days

$$\mathrm{it}\:\mathrm{can}\:\mathrm{be}\:\mathrm{solved}\:\mathrm{by}\:\mathrm{this}\:\mathrm{way}\:: \\ $$$$\mathrm{in}\:\mathrm{1}\:\mathrm{day}\:\mathrm{A}\:\mathrm{can}\:\mathrm{do}\:=\:\frac{\mathrm{1}}{\mathrm{10}}\:\mathrm{part}\:\mathrm{of}\:\mathrm{work} \\ $$$$\mathrm{in}\:\mathrm{1}\:\mathrm{day}\:\mathrm{B}\:\mathrm{can}\:\mathrm{do}\:=\:\frac{\mathrm{1}}{\mathrm{15}}\:\mathrm{part}\:\mathrm{of}\:\mathrm{work} \\ $$$$\mathrm{in}\:\mathrm{1}\:\mathrm{day}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{can}\:\mathrm{do}\:=\:\frac{\mathrm{1}}{\mathrm{10}}+\frac{\mathrm{1}}{\mathrm{15}}=\frac{\mathrm{1}}{\mathrm{6}}\:\mathrm{part}\:\mathrm{of}\:\mathrm{work} \\ $$$$\mathrm{so}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{can}\:\mathrm{do}\:\mathrm{the}\:\mathrm{work}\:\mathrm{in}\:\mathrm{6}\:\mathrm{days} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com