Question
In a survey of 200 people: 112 like coffee (C), 125 like
tea (T), 90 like juice (J). 60 like both C and T, 55 like T and J, 52 like C and J. If 30 like all three, how many like exactly one drink?Solution
ATQ,
Use inclusion: |C∪T∪J| = 112 + 125 + 90 − 60 − 55 − 52 + 30 = 190. Let only C = 112 − 60 − 52 + 30 = 30. Only T = 125 − 60 − 55 + 30 = 40. Only J = 90 − 55 − 52 + 30 = 13. Exactly one = 30 + 40 + 13 = 83.
A company hires workers A, B, and C to finish a project. A can complete the project in 30 days, B can do it in 24 days, and C can complete it in 20 days...
A can do a piece of work in 15 days, B is 25% more efficient than A, and C is 40% more efficient than B. A and C work together for 3 days and then C lea...
A can complete a piece of work in 10 days. B in 15 days and C in 20 days. A and C worked together for two days and then A was replaced by B. In how many...
Three workers P1, P2 and P3 got work from the contractor. In 30 days, ‘P1’ completed 30% of work. ‘P2’ is 20% less efficient tha...
Ajay and Bheem collectively earned Rs.9,000 for completing a task, with Bheem's share being Rs.3,000. If Bheem can complete the work on his own in 48 da...
. If 3 goats or 5 sheep can graze a field in 56 days, then in how many days can 6 goats and 10 sheep graze the same field?
‘A’ can complete a work in 20 days and is 20% more efficient than ‘B’. ‘A’ and ‘B’ start the work together, but ‘A’ leaves after 10 ...
- C is 37.5% more efficient than A, and A is 60% more efficient than B. If A, B, and C together can complete a task in 40 days, how long will it take A alone...
12 men can finish a work in 20 days by working 6 hours a day. How many more men are needed to finish the work in 12 days by working 6 hours a day?
A and B together can finish a job in 12 days. B alone takes 30 days. How long will A and C together take to finish the same job if C does one-fourth of ...
