Ratio and Proportion in JNVST Arithmetic: The Concept Behind the Formula

A Ratio Is Not a Pair of Numbers, It's a Relationship

Ratio questions in JNVST arithmetic look mechanical, split an amount according to a given ratio, but the questions that show up in past papers usually add a twist where the total itself changes partway through, or where one part of the ratio is adjusted, and the student has to figure out what happens to the rest of the ratio as a result. Treating a ratio as a fixed pair of numbers rather than a relationship between quantities is where most of the marks get lost.

A Worked Example With a Changing Total

Consider: "The ages of two brothers are in the ratio 3:5. After 4 years, the younger brother's age becomes 15. What is the current age of the elder brother?" A student sometimes tries to divide 15 directly using the 3:5 ratio, getting an incorrect current age for the younger brother. The correct method recognises that 15 is the age after 4 years, not now, so the younger brother's current age is 15 minus 4, which is 11. Since the current ratio of ages is 3:5, and the younger brother's share, 5 parts, equals 11, each part equals 11 divided by 5. The method that matters here, recover the current value before applying the ratio, is exactly what the question is testing, regardless of whether the resulting numbers come out whole.

The Trap: Splitting the New Total Using the Old Ratio Blindly

The recurring trap in ratio and proportion questions is applying a ratio to a total or value at the wrong point in time, usually because that value is the most recently mentioned number in the sentence, without checking whether the ratio given applies to that exact value or to an earlier or later stage described in the same question.

Why This Error Is Easy to Miss

Ratio division itself, splitting a number into parts according to 3:5 or similar, is a clean, well-drilled mechanical step, and performing it correctly on some number feels like solving the question. The error sits entirely in which number gets divided, a decision made before the ratio math starts, so a correct-looking division of an incorrect number still produces a wrong final answer that feels procedurally sound.

A Habit That Keeps the Ratio Honest

Before dividing anything by a ratio, have your child write down, in one short sentence, exactly what moment in time or what specific quantity the ratio applies to, based on the question's wording:

• Does the ratio describe the situation now, or before some change described in the question?
• Is the total being split the same total the ratio was originally given for?

Answering these two questions on paper before dividing is what prevents ratio questions from being solved a step too early or a step too late.