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Question
In an envelope there are some 5 rupee notes and some 10 rupee notes. Total amount of these notes together is 350 rupees. Number of 5 rupee notes are less by 10 than twice number of 10 rupee notes. Then find the number of 5 rupee and 10 rupee notes.
Solution
Let the number of Rs 5 notes be x and the number of Rs 10 notes be y.
5x + 10y = 350 ...(I)
Number of 5 rupee notes are less by 10 than twice number of 10 rupee notes
∴ x = 2y – 10
∴ x – 2y = –10 ...(II)
Multiplying equation (II) by 5,
5x – 10y = –50 ...(III)
Adding equations (I) and (III)
5x + 10y = 350
+ 5x – 10y = –50
10x = 300
∴ x =`300/10`
∴ x = 30
Substituting x = 30 in equation (II),
x – 2y = –10
30 – 2y = –10
∴ 30 + 10 = 2y
∴ 40 = 2y
∴ y = `40/2`
∴ y = 20
Number of Rs 5 notes = 30, number of Rs 10 notes = 20
Notes
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