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Question

In a group of 75 students, each has at least one vehicle, except 10 students which have none of the three vehicles. There are 40 students who have a car, 30 have a scooter and 20 have a bike. Also, it is known that 11 students have both car and bike, 12 have both bike and scooter, and 12 have both car and scooter.

Q. How many students have all the three vehicles?

A
5
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B
6
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C
8
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D
10
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Solution

The correct option is D 10

It is given that,

Car = X = 40; Scooter = Y = 30; Bike = Z = 20; (d + g) = 12; (e + g) = 12; (f + g) = 11

As 10 students have none of the vehicles, hence n = 10; so T = GT – n = 75 – 10 = 65.

We know that:

X + Y + Z = T + (d + g) + (e + g) + (f + g) – g

40 + 30 + 20 = 65 + 12 + 12 + 11 – g

90 – 100 = - g , or g = 10.

1. (D) g = 10.

2. (C) As g = 10, hence d = 2, e = 2, f = 1.

As Car = (a + d + g + f) or 40 = (a + 2 + 10 + 1)

Hence, Only Car, i.e. a = 40 – 13 = 27.

3. (C) Only 2 vehicles = (d + e + f) = (2 + 2 + 1) = 5.


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