A and B together can complete a job in 2 days. A alone takes x + 6 days to complete the job, while B alone takes x + 24 days to complete the same job. 1.What is the value of x? 2.How many days will A alone take to complete the job?

Let time taken by A & B to do a job = x days so time taken by A to do the job = x + 6 days & time taken by B to do the job = x + 6 + 18 = x + 24 days; Hence 1/(x+6) +1/(x+24) = 1/x (x+6+x+24)/{(x+6)(x+24)} = 1/x (2x+30)/(x^2+30x+144) = 1/x 2x^2+30x = x^2 + 30x + 144 x^2 = 144 x = 12 days So time taken by A alone to do the job = x + 6 = 12 + 6 = 18 days Alternate Method :- Let time taken by A & B to do a job = x days so time taken by A to do the job = x + 6 days & time taken by B to do the job = x + 6 + 18 = x + 24 days; Then x = root of (6 × 24) = root of 144 = 12 days So time taken by A alone to do this job = x + 6 = 12 + 6 = 18 days.