If x/2 = y/3 = z/7 , then the value of (2x-5y+4z)/2y is

Option d: 17/6. Solution: Given that: x/2 = y/3 = z/7 Let us set these equal ratios to a common constant k : x/2 = y/3 = z/7 = k This gives the values of x, y, z in terms of k : x = 2k, y = 3k, z = 7k We want to evaluate the expression: 2x - 5y + 4z/2y Substitute the values of x, y, and z into the expression: 2(2k) - 5(3k) + 4(7k)/2(3k) Simplify the terms in the numerator and the denominator: Numerator = 4k - 15k + 28k = (4 - 15 + 28)k = 17k Denominator = 6k Now, divide the numerator by the denominator: 17k/6k = 17/6 This matches Option D. Hence, Option D is the correct answer.

If $x/2 = y/3 = z/7$, then the value of $(2x-5y+4z)/2y$ is

The correct answer is Option d: $17/6$. Given that: $$\frac{x}{2} = \frac{y}{3} = \frac{z}{7}$$ Let us set these equal ratios to a common constant $k$: $$\frac{x}{2} = \frac{y}{3} = \frac{z}{7} = k$$ This gives the values of $x, y, z$ in terms of $k$: $$x = 2k, \quad y = 3k, \quad z = 7k$$ We want to evaluate the expression: $$\frac{2x - 5y + 4z}{2y}$$ Substitute the values of $x, y,$ and $z$ into the expression: $$\frac{2(2k) - 5(3k) + 4(7k)}{2(3k)}$$ Simplify the terms in the numerator and the denominator: $$\text{Numerator} = 4k - 15k + 28k = (4 - 15 + 28)k = 17k$$ $$\text{Denominator} = 6k$$ Now, divide the numerator by the denominator: $$\frac{17k}{6k} = \frac{17}{6}$$ This matches **Option D**. Hence, **Option D** is the correct answer.

Ratio, Proportion, Indices, LogarithmMCQMTP Dec 2023 Series IIQuestion 861 of 305

All Questions

If $\displaystyle x/2 = y/3 = z/7$ , then the value of $\displaystyle (2x-5y+4z)/2y$ is

Options

\displaystyle 6/23

\displaystyle 23/6

\displaystyle 3/2

\displaystyle 17/6

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — $\displaystyle 17/6$

All Options:

A $\displaystyle 6/23$
B $\displaystyle 23/6$
C $\displaystyle 3/2$
D $\displaystyle 17/6$

Detailed Solution & Explanation

Given that:

\frac{x}{2} = \frac{y}{3} = \frac{z}{7}

Let us set these equal ratios to a common constant

\displaystyle k

\frac{x}{2} = \frac{y}{3} = \frac{z}{7} = k

This gives the values of

\displaystyle x, y, z

in terms of

\displaystyle k

x = 2k, \quad y = 3k, \quad z = 7k

We want to evaluate the expression:

\frac{2x - 5y + 4z}{2y}

Substitute the values of

\displaystyle x, y,

and

\displaystyle z

into the expression:

\frac{2(2k) - 5(3k) + 4(7k)}{2(3k)}

Simplify the terms in the numerator and the denominator:

\text{Numerator} = 4k - 15k + 28k = (4 - 15 + 28)k = 17k

\text{Denominator} = 6k

Now, divide the numerator by the denominator:

\frac{17k}{6k} = \frac{17}{6}

This matches **Option D**.
Hence, **Option D** is the correct answer.

About This Chapter: Ratio, Proportion, Indices, Logarithm

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Ratio, Proportion, Indices, Logarithms

This chapter covers Ratio, Proportion, Indices, Logarithms and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 5-7 Marks weightage. Focus on understanding core concepts rather than memorizing.

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If x/2=y/3=z/7\displaystyle x/2 = y/3 = z/7x/2=y/3=z/7, then the value of (2x−5y+4z)/2y\displaystyle (2x-5y+4z)/2y(2x−5y+4z)/2y is