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Question
A hundred rupee note was changed to ten rupee notes and twenty rupee notes, eight notes in all. How many tens and how many twenties?
A hundred rupee note was changed to ten rupee notes and twenty rupee notes, eight notes in all. How many tens and how many twenties?
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Solution
Total amount of money = Rs.100
Total number of ten and twenty rupee notes = 8
Let the total number of ten rupee notes be x.
The total number of twenty rupee notes = 8 − x
Total amount made by ten rupee notes = x × Rs.10 = Rs.10x
Total amount made by twenty rupee notes = (8 − x) × Rs.20
= Rs.20(8 − x)
= Rs (160 − 20x)
∴ 10x + 160 − 20x = 100
⇒ −10x = 100 − 160
⇒ −10x = −60
⇒ x = 
⇒ x = 6
8 − x = 8 − 6 = 2
Thus, the total number of ten and twenty rupee notes is 6 and 2 respectively.
Total amount of money = Rs.100
Total number of ten and twenty rupee notes = 8
Let the total number of ten rupee notes be x.
The total number of twenty rupee notes = 8 − x
Total amount made by ten rupee notes = x × Rs.10 = Rs.10x
Total amount made by twenty rupee notes = (8 − x) × Rs.20
= Rs.20(8 − x)
= Rs (160 − 20x)
∴ 10x + 160 − 20x = 100
⇒ −10x = 100 − 160
⇒ −10x = −60
⇒ x =
⇒ x = 6
8 − x = 8 − 6 = 2
Thus, the total number of ten and twenty rupee notes is 6 and 2 respectively.
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