A man had 170 currency notes in all, some of which were of ₹ 100 denominations and some of ₹ 50 denominations. The total amount of all these currency notes was ₹ 10000. How much amount did he have in the denominations of ₹ 50?

Solution 1 :
Let the number of ₹ 50 notes = x, then the number of ₹ 100 notes = (170 - x)
According to question.
50x + 100(170 - x) = 10000
divide by 50 the above equation, we will get
⇒ x + 2(170 - x) = 200
⇒ x + 340 - 2x = 200
⇒ -x = 200 - 340 = -140
⇒ x = 140
∴ Required amount ₹ 50 x 140
= ₹ 7000
Solution 2 :
Let the number of ₹ 50 notes = x and the number of ₹ 100 notes = y.
according to given question,
x + y = 170 .............(1)
50x + 100y = 10000............(2)
Divide the equation (2) by 10 , we will get
5x + 17y = 1000............(3)
Multiply the equation (1) by 5
5x + 5y = 850 ------------(4)
Subtract the (4) equation from (3) equation, we will get,
5x +10y - ( 5x + 5y ) = 1000 - 850
⇒ 5x +10y - 5x - 5y = 1000 - 850
⇒ 10y - 5y = 1000 - 850
⇒ 5y = 150
⇒ y = 150/5
⇒ y = 30
Number of ₹ 100 notes = y = 30;
since x + Y = 170
therefore x = 170 - y
⇒ x = 170 - 30
⇒ x = 140
Number of ₹ 50 notes = x = 140