Problem Set 16 – Mixed Word ProblemsClass 5 Maths · Chapter 4 Multiplication and Division · Problem Set 16 – Maharashtra Board

Summary: Problem Set 16 – Mixed Word Problems

A mixed problem needs more than one operation, such as multiplying first and then dividing.

First find what the question asks. Then ask: what do I need to know before I can find it?

Words like 'each' and 'per' usually mean multiply to get a total; 'shared equally' or 'in each row' usually mean divide.

To see whether money was gained or lost, compare the money spent with the money received and subtract the smaller from the bigger.

Check the final answer by working backwards, for example by multiplying the quotient by the divisor.

Key points to remember

• Read the question and write what is asked
• Plan the steps before you calculate
• Each / per → multiply to find a total
• Shared equally → divide
• Remaining → subtract
• Spent vs received: bigger − smaller tells how much more or less
• Shortfall = what is needed − what is there
• Check by working backwards

Problem Set 16 – Mixed Word Problems – Notes

1. Plan before you calculate

• Write the question in your own words: 'I must find …'.
• List the facts given in the problem.
• Decide the order of the steps — the answer of step 1 is used in step 2.

2. Multiply, then divide

• If you know how many in each group but need to make new groups, first find the total by multiplying.
• Then divide the total by the size of each new group.

3. Subtract, then share

• If some amount is used first and the rest is shared, subtract first.
• ₹5,000 − ₹3,200 = ₹1,800 left; shared equally by 4 children → ₹1,800 ÷ 4 = ₹450 each.

4. Did we get more or less money?

• Find the money spent (cost) and the money received (selling).
• 6 fans bought at ₹1,650 each cost 6 × 1,650 = ₹9,900. Sold for ₹10,500 → ₹600 more than spent.
• If the money received is smaller, the difference shows how much less was received.

5. Is it enough? Finding the shortfall

• Find how much is needed in all, then compare it with what is available.
• A tank holds 2,500 litres. 14 families use 180 litres each: 14 × 180 = 2,520 litres.
• 2,520 > 2,500, so it is not enough. Shortfall = 2,520 − 2,500 = 20 litres.

Formulas at a glance

Key terms

Problem Set 16 – Mixed Word Problems – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 16 – Mixed Word Problems – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 16 – Mixed Word Problems

⏱ About 30 minutes

1. Plan (5 min)
   For each problem write 'I must find …' and list the steps.
2. Solve (20 min)
   Work out the example and the 4 'Try it yourself' problems.
3. Check (5 min)
   Work backwards to check, then take the quiz and play 🎮 Play.