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?
Correct Answer :
₹ 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:
(Equation 1)
From statement 3, Q purchased 5 notebooks less than P did:
(Equation 2)
Substituting Equation 2 into Equation 1:
Substituting the value of p into Equation 2:
From statement 5, P purchased 5 notebooks more than X did:
From statement 1, Z purchased 8 notebooks more than X did:
From statement 4, X and Y together purchased 28 notebooks:
Now, let's find the total number of notebooks purchased by all five friends:
Since each notebook is priced at ₹ 40, the total cost of all the notebooks is:
Therefore, the total cost of all the notebooks is ₹ 2,600.
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