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