Question
"Arnav, Bhanu, and Chinu can
finish a task in 18 days, 24 days, and 30 days, respectively. They all begin working together, but Bhanu stops after 4 days, and Arnav stops one day before the work is completed. How many days will it take to complete the work?"Solution
ATQ, Let, total task be LCM (18, 24, 30) = 360 units Number of units of work done by Arnav in one day = 360 ÷ 18 = 20 units Number of units of work done by Bhanu in one day = 360 ÷ 24 = 15 units Number of units of work done by Chinu in one day = 360 ÷ 30 = 12 units Number of units of work done by (Arnav + Bhanu + Chinu) in 4 days = (20 + 15 + 12) × 4 = 188 units Remaining work = 360 – 188 = 172 units Let, 'n' be the number of days for completion of task. (n – 4 – 1) × 20 + (n – 4) × 12 = 172 20n – 100 + 12n – 48 = 172 32n = 320 n = 320/32 n = 10 So, the task gets completed in 10 days
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