Profit and Loss in JNVST Arithmetic: A Section-by-Section Walkthrough

Cost Price Is Not Always the First Number You See

Profit and loss questions in JNVST arithmetic are built on a single relationship, profit or loss is always calculated as a percentage of the cost price, unless the question explicitly says otherwise. Going through past papers, the mistakes rarely come from not knowing this rule. They come from a question that never labels which number is the cost price and which is the selling price, and a student who assumes the first number mentioned is the cost price by default.

A Worked Example With a Hidden Cost Price

Consider: "A shopkeeper sold a toy for 240 rupees and made a profit of 20 percent. What was the cost price of the toy?" A student who assumes 240 is the cost price will calculate 20 percent of 240, add it to 240, and give an answer well above the actual cost price. But 240 here is the selling price, the price after profit was added, not before. The correct method sets up cost price as an unknown, recognises that selling price equals cost price plus 20 percent of cost price, which is 1.2 times the cost price, and then divides 240 by 1.2 to get a cost price of 200.

The Trap: Treating the Given Number as Cost Price by Default

This is the recurring trap in profit and loss questions: whichever number the sentence gives, students treat as the cost price and apply the percentage directly to it, regardless of what the sentence actually says was sold for how much. When the given number happens to be the selling price, as it often is in "sold for" questions, this produces a number that is arithmetically valid for a different question than the one being asked.

Why the Selling-Price Version Feels Natural

Multiplying a number by a percentage and adding it on is the most drilled operation in this chapter, so it is the first thing that comes to hand, and applying it to whatever number appears first in the sentence feels efficient rather than careless. The answer often lands close to a "reasonable" price for the item too, which removes the intuitive red flag that would normally make a student double check.

A Habit Built Around Labeling

Before any calculation, have your child write "CP =" and "SP =" on scratch paper and fill in only what the question actually states, leaving the unknown one blank:

• If the question says "sold for," that number goes next to SP.
• If the question says "bought for" or "cost him," that number goes next to CP.
• Whichever line is blank is the one being solved for, and the percentage always attaches to CP unless the question says the percentage is on SP.

This labeling step is slower than jumping straight to a percentage calculation, but it removes the single biggest source of profit and loss errors we see in our own practice data.