Question

Sunita has some ₹ 50 and ₹ 100 notes amounting to a total of ₹15,500. If the total number of notes is 200, the find how many notes of ₹ 50 and ₹ 100 each, she has.

Answer 1

Let the number of ₹ 50 notes be x and ₹100 notes be y.
x+ y = 200………..(1)

Total value of ₹ 50 notes= 50 × x = 50x
Total value of ₹ 100 notes= 100 × x = 100y

50x + 100y = 15500
50( x+ 2y) = 15500
x+ 2y = 15500/50
x+ 2y = 310…………(2)

Subtracting eq 1& 2
x + y = 200
x + 2y = 310     [by elimination method]
(-) (-)     (-)
------------------
-y = - 110
y = 110

On putting the value of y in equation 1
x+ y = 200
x + 110 = 200
x = 200-110
x = 90

Hence, she has ₹ 50 notes = 90 &  ₹100 notes = 110.

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Answer 2

Total number of notes = 200
Let Rs 50 notes be x

Rs 100 notes =200 - x

Value of :

Rs 50 notes = 50 × x = 50x

Rs 100 notes = 100(200 - x ) = Rs 20000 - 100x

Total amount = Rs 15,500

So by forming an equation,
we have,

50x + 20000 - 100x = 15500

-50x = 15500 - 20000

- 50x = - 4500


cancelling the - sign, we are left with

50x = 4500
$x = \frac{4500}{50}$

x = 90

Therefore,

Rs 50 notes = x = 90

Rs 100 notes = 200 - x = 200 - 90 = 110