Question

A can do a piece of work in 10 days and B in 20 days. They begin together but A leaves 2 days before the completion of the work. In how many days will the whole work be completed???​

Answer 1

Answer:

ᴄᴀɴ ᴅᴏ ᴀ ᴘɪᴇᴄᴇ ᴏꜰ ᴡᴏʀᴋ ɪɴ 10 ᴅᴀʏꜱ, ꜱᴏ ᴀ’ꜱ ᴅᴀɪʟʏ ᴄᴀᴘᴀᴄɪᴛʏ ɪꜱ 1/10 ᴘᴀʀᴛ ᴏꜰ ᴛʜᴇ ᴡᴏʀᴋ.

ʙ ᴄᴀɴ ᴅᴏ ᴛʜᴇ ꜱᴀᴍᴇ ᴡᴏʀᴋ ɪɴ 20 ᴅᴀʏꜱ, ꜱᴏ ʙꜱ ᴅᴀɪʟʏ ᴄᴀᴘᴀᴄɪᴛʏ ɪꜱ 1/20 ᴘᴀʀᴛ ᴏꜰ ᴛʜᴇ ᴡᴏʀᴋ ᴏʀ ᴇxᴀᴄᴛʟʏ ʜᴀʟꜰ ᴏꜰ ᴀ.

ʙᴏᴛʜ ꜱᴛᴀʀᴛᴇᴅ ᴛᴏɢᴇᴛʜᴇʀ ᴀɴᴅ ᴛʜᴇɪʀ ᴊᴏɪɴᴛ ᴄᴀᴘᴀᴄɪᴛʏ ᴡᴀꜱ …

1/10 + 1/20 = 3/20 ᴘᴀʀᴛꜱ ᴅᴀɪʟʏ ᴏꜰ ᴛʜᴇ ᴡʜᴏʟᴇ ᴡᴏʀᴋ. ɪᴛ ᴍᴇᴀɴꜱ ʙᴏᴛʜ ᴄᴏᴜʟᴅ ʜᴀᴠᴇ ᴄᴏᴍᴘʟᴇᴛᴇᴅ ᴛʜᴇ ᴡᴏʀᴋ ɪɴ 1/(3/20) = 20/3 ᴅᴀʏꜱ. ɪᴛ ᴍᴇᴀɴꜱ 6 ᴀɴᴅ 2/3 ᴅᴀʏꜱ ᴏʀ ɪɴ ᴛᴇʀᴍꜱ ᴏꜰ ɴᴜᴍʙᴇʀ ᴏꜰ ᴅᴀʏꜱ, ᴛᴇᴄʜɴɪᴄᴀʟʟʏ ɪᴛ ꜱʜᴏᴜʟᴅ ʙᴇ 7 ᴅᴀʏꜱ.

ᴀɴᴅ ᴡʜᴇɴ ʏᴏᴜ ꜱᴀʏ ᴀ ʟᴇꜰᴛ ᴛʜᴇ ᴡᴏʀᴋ 2 ᴅᴀʏꜱ ʙᴇꜰᴏʀᴇ ᴄᴏᴍᴘʟᴇᴛɪᴏɴ ᴏꜰ ᴛʜᴇ ᴡᴏʀᴋ ᴛʜᴀᴛ ɪᴍᴘʟɪᴇꜱ ᴛʜᴀᴛ ᴀ ᴡᴏʀᴋᴇᴅ ᴊᴏɪɴᴛʟʏ ᴡɪᴛʜ ʙ ꜰᴏʀ 5 ᴅᴀʏꜱ ᴀɴᴅ ʜᴀᴅ ᴄᴏᴍᴘʟᴇᴛᴇᴅ 1/2 ᴛʜᴇ ᴡᴏʀᴋ (5/10=1/2), ᴀɴᴅ ʙ ᴛᴏᴏ 5/20 = 1/4 ᴘᴀʀᴛ ᴏꜰ ᴛʜᴇ ᴡʜᴏʟᴇ ᴡᴏʀᴋ.

ᴀᴛ ᴛʜɪꜱ ᴘᴀʀᴛɪᴄᴜʟᴀʀ ᴘᴏɪɴᴛ ɪɴ ᴛɪᴍᴇ ᴛʜᴇ ᴡᴏʀᴋ ʟᴇꜰᴛ ᴡᴀꜱ 1 - (1/2 + 1/4) = 1/4 ᴘᴀʀᴛ ᴏɴʟʏ. ʙ ʙʏ ʜɪꜱ ɪɴᴅɪᴠɪᴅᴜᴀʟ ᴄᴀᴘᴀᴄɪᴛʏ ᴛʜɪꜱ ᴘᴀʀᴛ ᴡᴀꜱ ᴄᴏᴍᴘʟᴇᴛᴇᴅ ɪɴ 5 ᴅᴀʏꜱ, ɪ.ᴇ.(1/4)/(1/20). ɴᴏᴡ ꜱɪɴᴄᴇ ʙ ʜᴀᴅ ᴄᴏᴍᴘʟᴇᴛᴇᴅ ᴛʜᴇ ʀᴇᴍᴀɪɴɪɴɢ ɪɴ 5 ᴅᴀʏꜱ ᴀɴᴅ ᴀ ʜᴀᴅ ᴡᴏʀᴋᴇᴅ ꜰᴏʀ 5 ᴅᴀʏꜱ, ᴛʜᴇ ᴡʜᴏʟᴇ ᴡᴏʀᴋ ᴡᴀꜱ ᴄᴏᴍᴘʟᴇᴛᴇᴅ 5+5=10 ᴅᴀʏꜱ.

hope it helps u