A survey of 250 adults found that during the last year, 70 traveled by plane but not by train, 70 traveled by train but not by plane, 20 traveled by bus but not by plane or by train, 45 traveled by bus and plane, 20 traveled by all three, and 185 traveled by plane or train. How many did not travel by any of these modes of transportation? and plane, 20 traveled by all three, and 15 traveled by blanc eled by plane but not by train, 95

Question

14-09-2019
Mathematics

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A survey of 250 adults found that during the last year, 70 traveled by plane but not by train, 70 traveled by train but not by plane, 20 traveled by bus but not by plane or by train, 45 traveled by bus and plane, 20 traveled by all three, and 185 traveled by plane or train. How many did not travel by any of these modes of transportation? and plane, 20 traveled by all three, and 15 traveled by blanc eled by plane but not by train, 95

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jitenderchoubey81 jitenderchoubey81 · Answer 1 · 2019-09-20T07:00:46+02:00

Answer:

People who didn't travel by any mode = 45

Step-by-step explanation:

In the question,

Total number of people included in survey = 250

People who traveled by plane but not by train = 70

i.e.

a + e = 70

People who traveled by train but not by plane = 70

i.e.

c + d = 70

People who traveled by Bus but not by Plane or Train = 20

i.e.

f = 20 ..........(1)

People who traveled by bus and plane both = 45

i.e.

e + g = 45

People who traveled by all three = 20

i.e.

g = 20

People who traveled by Plane or Train = 185

i.e.

a + b + c + d + e + g = 185 ........(2)

So,

e = 45 - g = 45 - 20 = 25

e = 25

Now, on putting in eqn. (2) we get,

a + b + c + d + 25 + 20 = 185

a + b + c + d = 140 .......(3)

Now,

We need to find out,

Number of people travelling with any of these three is,

a + b + c + d + e + f + g

So,

On putting from eqn. (3) and (1), we get,

a + b + c + d + e + f + g = 140 + 25 + 20 + 20 = 205

So,

Number of people who didn't travel by any mode =Total people - Number of people travelling by any three

People who didn't travel by any mode = 250 - 205 = 45