Question
If 5 books cost ₹150, what is the cost of 8 books?
This is a classic unitary method problem — one of the most reliable scoring topics in Class 6 and 7 arithmetic.
Solution — Step by Step
We have 5 books for ₹150. To find the cost of 1 book, we divide the total cost by the number of books.
Now that we know 1 book costs ₹30, we multiply by 8 to get the cost of 8 books.
The cost of 8 books is ₹240.
Always re-read the question to confirm you answered what was actually asked — cost of 8 books, not 1 book.
Why This Works
The unitary method works because price and number of books are in direct proportion — more books, more cost. The rate (price per book) stays constant throughout.
We reduce the problem to “1 unit” first because 1 is the easiest number to scale from. Once we know the value of 1, we can find the value of any quantity by simply multiplying.
This two-step pattern — divide to find 1, multiply to find many — works for almost every unitary method problem in your textbook.
Alternative Method (Ratio Approach)
We can also set up a direct proportion:
Cross-multiplying:
Same answer, different route. The unitary method is faster here, but the ratio/proportion setup is useful when the numbers don’t divide cleanly.
For direct proportion problems, you can also use a quick mental check: 8 books is 1.6 times 5 books, so the cost should be 1.6 × ₹150 = ₹240. This is a great way to verify your answer in the last 30 seconds of an exam.
Common Mistake
Many students multiply first and divide later — writing ₹150 × 8 ÷ 5. While this gives the right answer mathematically, it’s risky with larger numbers and hides the logic. Always find the cost of 1 unit first, then scale up. If the question asked for 3 books instead of 8, the “multiply first” shortcut breaks down mentally. Build the correct habit now.