Menu Close

If-A-can-complete-2-5-th-of-a-work-in-24-days-and-B-can-complete-1-3-rd-of-the-work-in-30-days-then-in-how-many-days-can-they-complete-the-work-if-they-work-together-




Question Number 7485 by Obenfo last updated on 31/Aug/16
If A can complete (2/5)th of a work in 24  days and B can complete (1/3)rd of the  work in 30 days, then in how many days  can they complete the work if they work  together?
$$\mathrm{If}\:\mathrm{A}\:\mathrm{can}\:\mathrm{complete}\:\frac{\mathrm{2}}{\mathrm{5}}\mathrm{th}\:\mathrm{of}\:\mathrm{a}\:\mathrm{work}\:\mathrm{in}\:\mathrm{24} \\ $$$$\mathrm{days}\:\mathrm{and}\:\mathrm{B}\:\mathrm{can}\:\mathrm{complete}\:\frac{\mathrm{1}}{\mathrm{3}}\mathrm{rd}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{work}\:\mathrm{in}\:\mathrm{30}\:\mathrm{days},\:\mathrm{then}\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{days} \\ $$$$\mathrm{can}\:\mathrm{they}\:\mathrm{complete}\:\mathrm{the}\:\mathrm{work}\:\mathrm{if}\:\mathrm{they}\:\mathrm{work} \\ $$$$\mathrm{together}? \\ $$
Answered by sandy_suhendra last updated on 31/Aug/16
A can complete the work in = (5/2)× 24 days = 60 days  in 1 day A can complete = (1/(60)) of the work  B can complete the work in = (3/1)× 30 days = 90 days  in 1 day B can complete = (1/(90)) of the work  in 1 day A and B together can complete = (1/(60))+(1/(90)) = ((10)/(360)) = (1/(36)) of the work  so A and B together can complete the work in 36 days
$${A}\:{can}\:{complete}\:{the}\:{work}\:{in}\:=\:\frac{\mathrm{5}}{\mathrm{2}}×\:\mathrm{24}\:{days}\:=\:\mathrm{60}\:{days} \\ $$$${in}\:\mathrm{1}\:{day}\:{A}\:{can}\:{complete}\:=\:\frac{\mathrm{1}}{\mathrm{60}}\:{of}\:{the}\:{work} \\ $$$${B}\:{can}\:{complete}\:{the}\:{work}\:{in}\:=\:\frac{\mathrm{3}}{\mathrm{1}}×\:\mathrm{30}\:{days}\:=\:\mathrm{90}\:{days} \\ $$$${in}\:\mathrm{1}\:{day}\:{B}\:{can}\:{complete}\:=\:\frac{\mathrm{1}}{\mathrm{90}}\:{of}\:{the}\:{work} \\ $$$${in}\:\mathrm{1}\:{day}\:{A}\:{and}\:{B}\:{together}\:{can}\:{complete}\:=\:\frac{\mathrm{1}}{\mathrm{60}}+\frac{\mathrm{1}}{\mathrm{90}}\:=\:\frac{\mathrm{10}}{\mathrm{360}}\:=\:\frac{\mathrm{1}}{\mathrm{36}}\:{of}\:{the}\:{work} \\ $$$${so}\:{A}\:{and}\:{B}\:{together}\:{can}\:{complete}\:{the}\:{work}\:{in}\:\mathrm{36}\:{days} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *