Question

If \(A: B: C=1:4: 7 \) and \(B = (2x) % \)\(%\)\(\%\)of \((A+C)\), then \(x \) is :

• A. 12
• B. 25
• C. 30
• D. 45

Answer 1

The Correct Option is B

Let's solve the problem step by step. Given the ratio \(A:B:C=1:4:7\), this implies that \(A=1k\), \(B=4k\), \(C=7k\) for some constant \(k\). According to the problem, \(B=(2x)\%\) of \((A+C)\). Therefore, we can write:

\(B=\frac{2x}{100}\times(A+C)\)

Substituting the values of \(A\), \(B\), and \(C\) from the ratio:

\(4k=\frac{2x}{100}\times(1k+7k)\)

Simplifying:

\(4k=\frac{2x}{100}\times8k\)

To eliminate \(k\), divide both sides by \(k\):

\(4=\frac{16x}{100}\)

Solving for \(x\), multiply both sides by \(100\):

\(400=16x\)

Finally, divide both sides by \(16\) to find \(x\):

\(x=25\)

Therefore, the value of \(x\) is 25.