What must be added to each term of the ratio 7 : 11 to make it equal to 3 : 4?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5
Let the number added to each term be \(x\). The new ratio \((7+x):(11+x)\) must equal \(3:4\), and two equal ratios give equal cross products.
The new ratio equal to 3 : 4: \(\displaystyle\frac{7+x}{11+x}=\frac{3}{4}\)
Equal cross products: \(4(7+x)=3(11+x)\)
\(28+4x=33+3x\)
So the number to be added is \(x=5\)
Shortcut:
3 : 4 has a difference of 1 part, and the difference of the terms, \(11-7=4\), does not change when the same number is added to both
So 1 part is 4, and the new terms are \(3\times4=12\) and \(4\times4=16\): the number added is \(12-7=5\)