Question

Solve the following problems using two variables.
(vi) Durga's mother gave some 10 rupee notes and some 5 rupee notes to her, which amounts to Rs 190. Durga said,' if the number of 10 rupee notes and 5 rupee notes would have been interchanged, I would have Rs 185 in my hand.' So how many notes of rupee 10 and rupee 5 were given to Durga ?

Answer 1

Let the numbers of 10 rupee notes and 5 rupee notes be x and y, respectively.
According to the question, we have:
10x + 5y = 190
⇒ 5(2x + y) = 190
⇒ 2x + y = 38 ...(1)
and
5x + 10y = 185
⇒ 5(x + 2y) = 185
⇒ x + 2y = 37 ...(2)
Multiplying equation (1) by 2, we get:
4x + 2y = 76 ...(3)
Subtracting (2) from (3), we get:
4x + 2y = 76
x + 2y = 37
$-$ $-$ $-$
-----------------------
3x = 39
⇒ x = 13
Substituting the value of x in equation (1), we get:
2(13) + y = 38
⇒ 26+ y = 38
⇒ y = 12

Thus, number of 10 rupee notes = 13
Also, number of 5 rupee notes = 12