Kartik’s mother asked him to get the vegetables, milk and butter from the market and gave him the money in the denomination of 1 Rupee, 2 Rupee and 5 Rupee coins. Kartik first goes to the grocery shop to buy vegetables. At the grocery shop he gives half of his 5 Rupee coins and in return receives the same number of 1 Rupee coins. Next he goes to a dairy shop to buy milk and butter and gives all 2 Rupee coins and in return gets thirty 5 Rupee coins which increases the number of 5 Rupee coins to 75% more than the original number. If the number of 1 Rupee coins now is 50, the number of 1 Rupee and 5 Rupee coins originally were:

Let the number of 1 rupee , 2 rupee and 5 rupee coins be x, y and z respectively

At the grocery store he gives half of his 5 Rupee coins and in return receives the same number of 1 Rupee coins i.e z now become 0.5z and x now becomes x+0.5z

At the dairy store he gives all 2 Rupee coins and in return gets thirty 5 Rupee coins which increases the number of 5 Rupee coins to 75% more than the original number i.e now y = 0 and 0.5z = 0.5z+30

Also given 0.5z+30 = 1.75z

i.e. z=24

Also given that number of 1 Rupee coins now is 50 i.e. x+0.5z = 50 

i.e. x = 38

Therefore the number of 1 Rupee and 5 Rupee coins originally were 38 and 24 respectively. 

Therefore our answer is Option 'D'