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Q10·CSAT · Prelims 2026

Ratios — Compound Proportionality

NumericalRatio & ProportionArithmetic ProblemMedium

Question

Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x^2 and x is inversely proportional to z. For z= rac{7}{25}, the values of x and y are 5 and 50, respectively. If y=98, what is z equal to?

Options

a

\frac{1}{7}

b

\frac{1}{5}

Answer
c

\frac{5}{7}

d

1

Explanation

Let us translate the proportional relationships into mathematical equations:

1y \propto x² \implies y = k_1 x²
2x \propto 1/z \implies x = k_2/z \implies xz = k_2

Let us find the constant values using the initial data (z = 7/25, x = 5, y = 50):

From equation 1: 50 = k_1 (5)² \implies 50 = 25 k_1 \implies k_1 = 2
From equation 2: k_2 = x × z = 5 × 7/25 = 7/5

Now, substitute the new value y = 98 to find the corresponding value for z:

98 = 2 x² \implies x² = 49 \implies x = 7 (since values must be positive real numbers)
Substitute x = 7 into the inverse variation equation xz = k_2:

7 × z = 7/5 \implies z = 1/5

Setting up explicit equations for proportional relationships allows solving for unknown values across changing datasets.

Answer: (b).

Question details

Year

2026

Paper

CSAT

Question

Q10

Section

Quantitative Aptitude

Sub-topic

Ratio & Proportion

Type

Arithmetic Problem

Difficulty

Medium

Source hint

Standard variation — proportional constant determination

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