P and Q can individually complete a piece of work in 15 and 25 days respectively. In how many days can P and Q complete the work if they work on alternate days? (a) Starting with P (b) Starting with Q Share with your friends Share 1 Shruti Tyagi answered this Dear Student, let the total work done be LCM(15,25)=75 unitsnow P's one day work=7515 =5Q's one day work=7525=3total work done in 2 days=5+3=8so in 2 days 8 units of work is completed⇒728=9in 9 such blocks of 2 days about 72 units of work will be completedi.e total number of days =9×2 =18now still remaining work=75-72=3 unitsthis 3 units of work will be done by P or Q depending on who started firsta) starting with Pwhen P started working on day 1, his turn will repeat on day 3,5,7,9.. 19hence day 19 P will worktime required to complete 3 units of work=35Total time taken =18+35=1835b) starting with Qwhen Q started work on first day, his turn will repeat on day 3,5,7,9.. and 19hence again on day 19, Q will worktime taken to complete remaining 3 units of work for Q=33=1Hence total number of days=18+1=19 Regards, 1 View Full Answer
