### Life Mathematics Class 8th Mathematics Term 3 Tamilnadu Board Solution

##### Question 1.A man can complete a work in 4 days, whereas a woman can complete it in only12 days. If they work together, in how many days, can the work be completed?Answer:A man can complete a work in 4 daysMan’s 1-day work = Woman can complete a work in 12 daysWoman’s 1-day work = 1-day work of both = + = By working together, they can complete a work in 3 daysQuestion 2.Two boys can finish a work in 10 days when they work together. The first boy can do it alone in 15 days. Find in how many days will the second boy do it all himself?Answer:If two boys work together they can finish a work in 10 daysLet the two boys be x & yx & y’s 1-day work = x + y = ..eq (1)first boy (x) can do it in 15 daysx’s 1-day work = x = substituting the value of x in eq(1)x + y =  + y = y = y’s 1-day work = so, second boy (y) can do a work in 30 daysQuestion 3.Three men A, B and C can complete a job in 8, 12 and 16 days respectively.A and B work together for 3 days; then B leaves and C joins. In how many days, can A and C finish the work?Answer:A, B and C can complete a job in 8, 12 and 16 days respectively.1-Day work:A’s = B’s = C’s = A and B’s 1-day work = + = A and B work together for 3 days= 3 × = The remaining work after 3 days = 1- = The remaining work will be done by A & C togetherWork done by A & C = By doing potion of the work in a day they can complete remaining work ( ) in 2 daysQuestion 4.A tap A can fill a drum in 10 minutes. A second tap B can fill in 20 minutes. A third tap C can empty in 15 minutes. If initially the drum is empty, find when it will be full if all taps are opened together?Answer:Time taken by A = 10 minWork done by A in 1 min = Time taken by B = 20 minWork done by B in 1 min = Time taken by C = 15 minWork done by C in 1 min = Work done by all three A, B & C in 1 min = + - = Time taken by all three A, B & C in = 12 minQuestion 5.A can finish a job in 20 days and B can complete it in 30 days. They work together and finish the job. If Rs. 600 is paid as wages, find the share of each.Answer:Time taken by A = 20 daysWork done by A in 1 day = Time taken by B = 30 daysWork done by B in 1 day = Wages = 600Ratio of work done by A & B in 1-day = : = 3:2So. The ratio of the wages will be 3:23x + 2x = 6005x = 600X = 120A’s wage = 3x = 3 × 120 = 360B’s wage = 2x = 2 × 120 = 240Question 6.A, B and C can do a work in 12, 24 and 8 days respectively. They all work for one day. Then C leaves the group. In how many days will A and B complete the rest of the work?Answer:A, B and C can do a work in 12, 24 and 8 days respectively.A, B and C’s 1-day work will be , , respectively1-day’s work of all of them = + + = Remaining portion of work = 1- = After that C leaves the group. So, the rest of the work will be completed by A & B onlyA & B’s 1-day’s work = + = No. of day required = = = 6 daysQuestion 7.A tap can fill a tank in 15 minutes. Another tap can empty it in 20 minutes. Initially the tank is empty. If both the taps start functioning, when will the tank become full?Answer:Time taken by A = 15 minWork done by A in 1 min = Time taken by B = 30 minWork done by B in 1 min = Work done by all three A, B in 1 min = - = (∵ B empties the tank we use negative there)Time taken to fill to the tank is 60 min

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