some doubts in set (Venn diagram): how many read papers?

[defeated_soldier]

Problem: In a sample of newspaper readers, 42 read the Times of India (ToI), 46 read the Indian Express (IE) and 53 read Midday (M). Everybody in the sample of 111 reads at least one paper, and 27 read more than one daily.

Q1. How many read all three papers?

Q2. If 10 people read only two dailies – IE and M, how many people read only ToI?

My approach:

here is my figure

As per this figure,

Q1: i need to find d .

I have eqn:

x+y+z+a+b+c+d=111 ...(1)

a+b+c+d=27........(2)

x+a+d+b=42.....(3)

y+a+d+c=46.....(4)

z+b+d+c=53......(5)

Now i am stuck completely ....i cant find d

what to do here ?

Q2: here i need to find x ( Only TOI) .

it says "10 people read only two dailies "

means ? if i take one people from this , can he read TOI and IE both ?
bit confused here.

 

[Deleted member 4993]

(3)+(4) + (5)

x + y + z + 2(a+b+c+d) + d = 141

(1) + (2)

x + y + z + 2(a+b+c+d) = 138

d = 3

Now continue...

 

[defeated_soldier]

thanks for the reply.
oops....i was so close but so far !

i was hoping from eqns to eqns but not thought that way.

can you please respond to the other question ?


Q2. If 10 people read only two dailies – IE and M, how many people read only ToI?

see they say "10 people read only two dailies"

what it means ?

suppose, 5 people read IE and 5 people read M , 5+5=10 // is it ok ?

supose , 10 people read IE and M Both // is it ok ?


i need to be clear here because i have to frame eqns with proper variables from the venn diagram.

please clarify this doubt.

thanks

defeated_soldier

 

[Deleted member 4993]

Q2. If 10 people read only two dailies – IE and M, how many people read only ToI?

c = 10

a + b + d = 27 -10

continue...

 

[defeated_soldier]

c = 10

ok.i go it.

that means each of the ten people read two dailies i.e IE and M.

the language killed me.

as question asks for only TOI

so 42-(a + b + d ) is the answer.

42-17=25 (ans)

thanks