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Q45·CSAT · Prelims 2022

Solving a system of linear equations to find total cost

NumericalAlgebra & EquationsFactual single● Medium

Question

Five friends P, Q, X, Y and Z purchased some notebooks. The relevant information is given below:

1Z purchased 8 notebooks more than X did.
2P and Q together purchased 21 notebooks.
3Q purchased 5 notebooks less than P did.
4X and Y together purchased 28 notebooks.
5P 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

Answer
b

2,400

c

2,360

d

2,320

Explanation

Translate the statements into an algebraic system to find individual totals: Eq 2: P + Q = 21 Eq 3: Q = P - 5 Substitute Eq 3 into Eq 2: P + (P - 5) = 21 \implies 2P = 26 \implies P = 13. Using P, find Q: Q = 13 - 5 = 8.

Eq 5: P = X + 5. Since P = 13, then 13 = X + 5 \implies X = 8. Eq 1: Z = X + 8. Since X = 8, then Z = 8 + 8 = 16. Eq 4: X + Y = 28. Since X = 8, then 8 + Y = 28 \implies Y = 20.

Calculate the total number of notebooks: Total = P + Q + X + Y + Z = 13 + 8 + 8 + 20 + 16 = 65 notebooks. Calculate total cost at ₹40 each: Cost = 65 × 40 = 2600.

For chain-linked variable puzzles, isolate the pair of equations containing the same two variables (like P and Q here) to break the system open and find your first exact value.

Answer: (a).

Question details

Year

2022

Paper

CSAT

Question

Q45

Section

Numerical Ability

Sub-topic

Algebra & Equations

Type

Factual single

Difficulty

Medium

Source hint

Five friends P, Q, X, Y, Z notebooks

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