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An amount of Rs 70 was required in change by the shopkeeper. He needed change in the denominations of Re. 1, 2 and 5 coins. How many coins will be required if they are in the ratio 5 ∶ 5 ∶ 4?
- a)35
- b)28
- c)14
- d)7
Correct answer is option 'B'. Can you explain this answer?
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An amount of Rs 70 was required in change by the shopkeeper. He needed...
Total amount = Rs 70
Ratio of coins respectively for 1, 2 and 5-rupee coins = 5 ∶ 5 ∶ 4
Let the no. of coins be 5x, 5x and 4x.
⇒ Total amount by 1-rupee coins = 1 × 5x = 5x ----(1)
⇒ Total amount by 2-rupee coins = 2 × 5x = 10x ----(2)
⇒ Total amount by 5-rupee coins = 5 × (4x) = 20x ----(3)
⇒ 5x + 10x + 20x = 70 (From (1), (2) and (3)) ----(4)
⇒ 35x = 70
⇒ x = 70/35 = 2
No. of 1-rupee coins = 5x = 5 × 2 = 10
No. of 2-rupee coins = 5x = 5 × 2 =
10No. of 5-rupee coins = 4x = 4 × 2 = 8
∴ Total no. of coins = 10 + 10 + 8 = 28.
Ratio of coins respectively for 1, 2 and 5-rupee coins = 5 ∶ 5 ∶ 4
Let the no. of coins be 5x, 5x and 4x.
⇒ Total amount by 1-rupee coins = 1 × 5x = 5x ----(1)
⇒ Total amount by 2-rupee coins = 2 × 5x = 10x ----(2)
⇒ Total amount by 5-rupee coins = 5 × (4x) = 20x ----(3)
⇒ 5x + 10x + 20x = 70 (From (1), (2) and (3)) ----(4)
⇒ 35x = 70
⇒ x = 70/35 = 2
No. of 1-rupee coins = 5x = 5 × 2 = 10
No. of 2-rupee coins = 5x = 5 × 2 =
10No. of 5-rupee coins = 4x = 4 × 2 = 8
∴ Total no. of coins = 10 + 10 + 8 = 28.
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