A merchant in the port city of Lothal is exchanging bags of spices for copper ingots. He receives 15 ingots for every 2 bags of spices. If he brings 12 bags of spices to the market, how many copper ingots will he leave with?
Step-by-step solution
To find: Number of ingots he receives
Idea: The rate is fixed: every 2 bags bring 15 ingots. Find how many groups of 2 bags are in 12 bags, then multiply by 15.
- Number of groups of 2 bags in 12 bags = 12 ÷ 2 = 6.½ mark
- Each group of 2 bags gives 15 ingots.½ mark
- Total ingots = 6 × 15 = 90.1 mark
Check: Ingots per bag = 15 ÷ 2 = 7.5, and 12 × 7.5 = 90 ✓.
Answer to write in the exam
2 bags → 15 ingots
Number of groups of 2 bags = 12 ÷ 2 = 6
Ingots = 6 × 15 = 90
∴ He leaves with 90 copper ingots.
Common mistakes that cost marks
- Multiplying 12 × 15 = 180, forgetting that 15 ingots are for 2 bags, not for 1 bag.
- Dividing the wrong way: 15 ÷ 12 or 12 ÷ 15 does not answer the question.
- Writing 7.5 ingots per bag and stopping there without multiplying by 12.
How this can come in the exam
A weaver gets 9 kg of cotton for every 4 shawls. How many kg of cotton does she get for 20 shawls?
- 36 kg
- 45 kg
- 80 kg
- 180 kg
Show answer
(B) 45 kg
20 ÷ 4 = 5 groups; 5 × 9 = 45 kg.
At a Harappan market, 3 clay pots can be exchanged for 8 strings of beads, and 2 strings of beads can be exchanged for 5 fish.
(i) How many strings of beads do 12 pots fetch? (ii) How many fish do 8 strings of beads fetch? (iii) How many fish can a potter get for 12 pots? (iv) How many pots are needed for 60 fish?
Show answer
(i) 12 ÷ 3 = 4 groups, 4 × 8 = 32 strings (1 mark). (ii) 8 ÷ 2 = 4 groups, 4 × 5 = 20 fish (1 mark). (iii) 32 strings = 16 groups of 2, 16 × 5 = 80 fish (1 mark). (iv) 60 fish = 12 groups of 5 → 24 strings = 3 groups of 8 → 3 × 3 = 9 pots (1 mark).Try one yourself
A farmer receives 10 measures of salt for every 3 baskets of grain. How many measures of salt does he get for 18 baskets?
Show answer
18 ÷ 3 = 6 groups; 6 × 10 = 60 measures.
More questions like this
- Look at the sequence of numbers on one column of the Ishango bone: 11, 13, 17, 19. What do these numbers have in common? List the next three numbers that fit this pattern.
- We know that Natural Numbers are closed under addition (the sum of any two natural numbers is always a natural number). Are they closed under subtraction? Provide a couple of examples to justify your answer.
- Ancient Indians used the joints of their fingers to count, a practice still seen today. Each finger has 3 joints, and the thumb is used to count them. How many can you count on one hand? How does this relate to the ancient base-12 counting systems?
- Brahmagupta did not stop at zero. He realised that if subtraction of a number from itself can result in zero (5 − 5 = 0), then what would happen if we subtracted a larger number from a smaller one (3 − 5 = □)?
- Why does a negative times a negative equal a positive? Think of it in terms of action and debt. If a negative number represents a debt, then multiplying by a negative number represents the removal of that debt.
(Hint: If someone takes away (−) four of your debts that are each worth ₹3 (that is, −3), you are effectively ₹12 richer! Therefore, (−3) × (−4) = +12.)