1. In a society of 345 persons, those who like Raga, Paltu and Namo as a leader are equal in numbers. There are 30 persons who like both Raga and Paltu, 26 who like both Paltu and Namo, 28 who like Namo and Raga and 14 who like all the leaders. There are 43 persons who didn’t like any of these three leaders. How many persons do like Raga as a leader?
115
124
246
108
2.A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
100m
150m
190m
200m
3.Advik and Billy can do a piece of work in 45 days and 40 days respectively. They began the work together but Advik leaves after some days and then Billy completed the remaining work in 23 days. The number of days after which Advik left the work was:
6
8
9
12
4.Akash leaves mumbai at 6 am and reaches Bangalore at 10 am . Prakash leaves Bangalore at 8 am and reaches Mumbai at 11:30 am. At what time do they cross each other?
10am
8.32am
8.56am
9.20am
5.In a society of 345 persons, those who like Raga, Paltu and Namo as a leader are equal in numbers. There are 30 persons who like both Raga and Paltu, 26 who like both Paltu and Namo, 28 who like Namo and Raga and 14 who like all the leaders. There are 43 persons who didn’t like any of these three leaders. How many persons do like only one leader?
286
124
246
108
Answers
Solution 2) :-
→ Speed of thief = 10 km/h
→ Speed of policeman = 11 km/h .
so,
→ Usual speed (in same direction) = 11 - 10 = 1 km/h .
then,
→ Distance covered in 60 minutes = 1000 m
→ Distance covered in 1 minute = 1000/60 m
→ Distance covered in 6 minutes = (1000/60) * 6 = 100 m .
therefore,
→ Distance between them after 6 minutes = Total distance between them - distance covered in 6 minutes = 200 - 100 = 100 m (Ans.)
Solution 3) :-
→ LCM of 45 and 40 = 360 units = Let total work .
so,
→ Efficiency of Advik = Total work / time taken = 360/45 = 8 unit / day .
→ Efficiency of Billy = Total work / time taken = 360/40 = 9 unit / day .
now, given that they began the work together but Advik leaves after some days and then Billy completed the remaining work in 23 days.
so, let us assume that, after x days Advik left the work .
then,
→ x * (Advik + Billy) + 23 * Billy = Total work
→ x(8 + 9) + 23 * 9 = 360
→ 17x + 207 = 360
→ 17x = 360 - 207
→ 17x = 153
→ x = 9 days (Ans.)
Solution 4) :-
Let us assume that, distance between mumbai and banglore is 2D km .
so,
→ Time taken by Akash from mumbai to banglore = 6AM to 8 AM = 4 hours .
→ Time taken by Prakash from banglore to mumbai = 8AM to 11:30 = 3.30 = 3(1/2) = (7/2) hours .
now, since from 6 AM to 8AM akash travels alone .
then,
→ Distance covered by akash in 2 hours = (2D/4) * 2 = D km .
now,
→ Distance left to be covered by both of them = 2D - D = D km .
and,
→ Usual speed now (opposite direction) = (2D/4) + (2D/7/2) = (D/2) + (4D/7) = (7D + 8D)/14 = (15D/14)
then,
→ Time taken by them to cross each other = D/S = D/(15D/14) = D * (14/15D) = (14/15) hours = (14/15) * 60 = 56 minutes .
therefore,
→ Time at which they will cross each other = 8 AM + 56 minutes = 8 : 56 AM (Ans.)
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