Subject
Quantitative Aptitude
Topic
Time and Work
2 children and 3 men can do a work in 12 days while 3 children and 2 men can do the same work in 10 days. How many days it will take to complete the same work if 1 child and 1 man work together?
2 children and 3 men can do a work in 12 days while 3 children and 2 men can do the same work in 10 days. How many days it will take to complete the same work if 1 child and 1 man work together?
ক)
27 daysখ)
\(\frac{3}{{11}}days\)গ)
\(27\frac{3}{{11}}days\)ঘ)
37 daysExplanation
Work done in 1 day by 2 children and 3 men, 2 C + 3 M = 1/12…………………(1) Work done in 1 day by 3 children and 2 men, 3 C + 2 M = 1/10…………………..(2) Solving equations (1) and (2) we get, Work done in one day by 1 man, M = 1/100 Work done in one day by 1 child, C = 2/75 Total Work done in one day by 1 man and 1 child = 1/100 + 2/75 = 11/300 Hence, total time taken by them to complete the whole work =300/11 = Alternate Method (Short Trick): Work done by 2 children and 3 man in 12 days = work done by 3 men and 2 children in 10 days, Or, (2C + 3M) × 12 = (3C + 2M) × 10 Or, 24C + 36M = 30C + 20M, Or, 16M = 6C, Or, M = 3C/8 Now, Work done by 2 children and 3 men in 12 days = work done by 1 man and 1 child in X days (let), ∴ (2C + 3M) × 12 = (M + C) × X, Putting the value of M in terms of C, (2C + 9C/8) × 12 = (3C/8 + C) × X Solving, daysRelated questions
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