Question

I have 2000 amount of 50 and 20 rupeess, the notes count is 64, how many 50 rupees note and how many 20 rupees note i have

Answer 1

Answer:

No. of Rs 50 notes = x

No. of Rs 20 notes = y

Total notes = 64

x + y = 64 [by number]

50x + 20y = 2000 [by amount]

There are two methods to solve this question:-

(i) Substitution Method:-

x + y = 64

x = 64 - y

50x + 20y = 2000

50(64 - y) + 20y = 2000

3200 - 50y + 20y = 2000

3200 - 30y = 2000

-30y = 2000 - 3200

-30y = -1200

y = 40

x = 64 - y

= 64 - 40

= 24

Rs 50 notes = 24

Rs 20 notes = 40

(ii) Subtraction Method:-

x + y = 64 — (i)

50x + 20y = 2000 — (ii)

To compare both these equations, we will first multiply the first equation by 50 because in the second equation, the first constant’s value is 50.

$50x + 50y = 3200 \\50x + 20y = 2000$

Now we will change the signs in the second equations due to subtraction.

$50x + 50y = 3200 \\-50x - 20y = -2000 \\\\30y = 1200 \\y = 40$

$x + y = 64 \\x + 40 = 64 \\x = 64 - 40 \\x = 24$

Rs 50 notes = 24

Rs 20 notes = 40

Verify:-

50x + 20y = 2000

50(24) + 20(40) = 2000

1200 + 800 = 2000

2000 = 2000

LHS = RHS

Hence, verified

Hope it helps

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