Question Details

Five friends P, Q, X, Y and Z purchased some notebooks. The relevant information is given below:
1. Z purchased 8 notebooks more than X did.
2. P and Q together purchased 21 notebooks.
3. Q purchased 5 notebooks less than P did.
4. X and Y together purchased 28 notebooks.
5. P purchased 5 notebooks more than X did.
If each notebook is priced ` 40, then what is the total cost of all the notebooks?

Options

A

₹ 2,600

B

₹  2,400

C

₹` 2,360

D

₹ 2,320

Show Answer

Correct Answer :

Option A

₹ 2,600

Solution :

The correct option is ₹ 2,600.

Let the number of notebooks purchased by P, Q, X, Y, and Z be represented by the variables p, q, x, y, and z respectively.

From the given information, we can construct the following system of equations:

From statement 2, P and Q together purchased 21 notebooks:
p+q=21 (Equation 1)

From statement 3, Q purchased 5 notebooks less than P did:
q=p-5 (Equation 2)

Substituting Equation 2 into Equation 1:
p+(p-5)=21
2p-5=21
2p=26
p=13

Substituting the value of p into Equation 2:
q=13-5=8

From statement 5, P purchased 5 notebooks more than X did:
p=x+5
13=x+5
x=8

From statement 1, Z purchased 8 notebooks more than X did:
z=x+8
z=8+8=16

From statement 4, X and Y together purchased 28 notebooks:
x+y=28
8+y=28
y=20

Now, let's find the total number of notebooks purchased by all five friends:
Total Notebooks=p+q+x+y+z
Total Notebooks=13+8+8+20+16=65

Since each notebook is priced at ₹ 40, the total cost of all the notebooks is:
Total Cost=65×40=2600

Therefore, the total cost of all the notebooks is ₹ 2,600.

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