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?
(UPSC CSE Prelims CSAT 2022)
(a). ₹2,600
(b). ₹2,400
(c). ₹2,360
(d). ₹2,320
Solution:
Let's represent the number of notebooks purchased by each friend with the respective letter (P, Q, X, Y, Z) and use algebra to solve for their values.
From statement 1, we know that:
Z = X + 8
From statement 2, we know that:
P + Q = 21
From statement 3, we know that:
Q = P - 5
From statement 4, we know that:
X + Y = 28
From statement 5, we know that:
P = X + 5
We can use these equations to solve for each variable. Starting with P and Q, we can substitute equation 3 into equation 2 to get:
P + (P - 5) = 21
2P - 5 = 21
2P = 26
P = 13
And since Q = P - 5, we have:
Q = 8
Next, we can substitute these values into equation 5 to get:
13 = X + 5
X = 8
Now we can use equations 1 and 5 to solve for Z and Y:
Z = X + 8 = 16
Y = 28 - X = 20
Therefore, P purchased 13 notebooks, Q purchased 8 notebooks, X purchased 8 notebooks, Y purchased 20 notebooks, and Z purchased 16 notebooks. The total number of notebooks purchased is:
13 + 8 + 8 + 20 + 16 = 65
The total cost of all the notebooks at ₹40 each is:
65 * 40 = ₹2,600
So the total cost of all the notebooks is ₹2,600.