(Q13).Rubina went to a bank to withdraw ₹2000. She asked the cashier to give the cash in ₹50 and ₹100 notes only. She got 25 notes in all. Can you tell how many notes each of ₹50 and ₹100 she received?

Let the number of ₹50 notes be x;

Let the number of ₹100 notes be y;

then, x + y = ...............(1)

and x + y = ...........(2)

Solutions through the substitution method:

From equation (1) ⇒ x = -

Substituting in equation (2) ⇒ 50 ( - ) + 100y = 2000

- y + 100y = 2000

50y = 2000 - =

y =
50
 =

x = - =

Hence, Rubina received ₹50 notes and ₹100 notes.

Solution through the elimination method:

In the equations, coefficients of x are 1 and 50 respectively. So,

Equation (1) × : x + y =
Equation (2) × : x + y = same sign, so subtract
(-) (-) (-)

-y = -

or y =
-
-
 =

Substitute y in equation (1) x + = 25

x = 25 - =

Hence Rubina received ₹50 notes and ₹100 rupee notes.