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Question
A bag contains ₹ 1,600 in the form of ₹10 and ₹20 notes. If the ratio between the numbers of ₹10 and ₹20 notes is 2 : 3; find the total number of notes in all.
Solution
Total amount in the bag = 1600
It contains notes in the denomination of ₹10 and 20
Ratio between the number of ₹10 and 20 notes is = 2 : 3
Let number of ₹10 note = x
and number of ₹ 20 notes = y
According to condition,
10x + 20y = 1600 ....(i)
and x = `2/3`y ....(ii)
Now, substitute the value of x in eq (i)
`10 xx 2/3"y" + 20"y" = 1600`
`=> 20/3 "y" + 20y = 1600`
`=> (20 + 60)/3 "y" = 1600`
`=> 80/3 "y" = 1600`
`=> "y" = (1600 xx 3)/80`
∴ y = 60
Now, substitute the value of y in eq (ii), we get
x = `2/3 xx 60 = 40`
Total nuber of notes in all = x + y
= 60 + 40 = 100 notes
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