The cost of a pen and a pencil used to be the same, but recently the cost of the pen was increased by ₹4, whereas, the cost of pencil became ₹6 less than 5 times its original value. After the revised cost, if the pen was more expensive than the pencil, what could have been the possible original value of both the products, if the initial price was a natural number?

The possible original values of both products are ₹2 or ₹1

Step-by-step explanation:

The question is a word problem leading to simultaneous equations

Let 'x' represent the initial value of the pen and pencil

Therefore;

The final cost of the pen = x + ₹4

The final cost of the pencil = 5·x - ₹6

x + ₹4 > 5·x - ₹6

∴  ₹4 + ₹6 > 5·x - x

₹10 > 4x

₹10/4 > x

₹2.5 > x

Given that x is a natural number, therefore

x ≤ ₹2

The possible original values of both products are ₹2 or ₹1

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction