Concept 2 of 3
Multi-Step Unitary: Find One, Scale Twice
Today's big idea
Go down to one, across to the other item, then up to the amount asked for.
Every step on its own is easy, and the skill is keeping them in order.
How it works
👀 What's going on?
Five notebooks cost 60 rupees, and a pen costs twice what a notebook costs. The question wants the price of twelve pens. No single sum gets you there, but a chain of easy ones does.
💡 Here's the trick
Go down to one, across, then back up. Divide to find the value of one of the first item. Use the link the question gives you to find one of the second. Then multiply up to the amount asked for. Every step on its own is a sum you can already do.
🪄 How to do it
- 1.Divide to find one unit of the first item in the picture above.
- 2.Use the link stated in the question to get one unit of the second item.
- 3.Multiply up to the quantity the question asks about.
✍️ Try it
5 notebooks cost 60 rupees and a pen costs twice a notebook, so what do 12 pens cost? And if 3 kg of rice feeds 12 people, how many people does 7 kg feed?
One notebook is 12 rupees, so one pen is 24, and 12 pens come to 288 rupees. For the rice, 1 kg feeds 4 people, so 7 kg feeds 28.
⚠️ Watch out
Some links run backwards. More workers means fewer days, not more, so 4 workers taking 6 days is really 24 days of work shared out. When the second quantity should fall as the first rises, multiply to find that fixed total first, then divide.
🌟 Why this matters
Scaling a recipe up for extra guests is this exact chain. So is working out whether the large packet really is better value than the small one.
Exam tip: Write the units beside each number as you go, so a price per notebook never gets multiplied by a count of pens.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“6 cups cost ₹90. A plate costs 3 times a cup. Cost of 5 plates?”
- 1
Step 1: cost of 1 cup
90 ÷ 6 = 15
- 2
Step 2: cost of 1 plate
Plate is 3 times a cup → plate = 15 × 3 = 45.
- 3
Step 3: 5 plates
45 × 5 = 225
- 4
Answer ✓
₹225
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Step 1: divide to find the value of ONE. Step 2: multiply by the quantity you need.
SHOP · ROUND 1 OF 3
6 apples = ₹48
Step 1 — divide to find ONE: ₹48 ÷ 6 = ?
Quick check
✅ VERIFICATION
6 workers finish a job in 10 days. How long would 12 workers take, working at the same rate?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Speed, Distance & Time
Speed is one hour's jump. Distance adds jumps, time counts them.