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.

Answer 1

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