The price of commodity X increases by 40 paise
every year, while the price of commodity Y
increases by 15 paise every year. If in 2004, the
price of commodity X was 4.20 and that of Y
was 6.30, in which year commodity X will cost
40 paise more than the commodity Y?

Question

Accepted Answer

Let $$ z $$ represent the number of years after 2004 when the price difference between commodity X and Y becomes 40 paise.

1. **Formulate the equation**:  
   The price of X after $$ z $$ years is $$ 4.20 + 0.40z $$, and the price of Y after $$ z $$ years is $$ 6.30 + 0.15z $$.  
   The condition for X being 40 paise more than Y is:  
   $$
   (4.20 + 0.40z) - (6.30 + 0.15z) = 0.40
   $$

2. **Simplify the equation**:  
   Combine terms:  
   $$
   0.25z = 0.40 + (6.30 - 4.20)
   $$  
   $$
   0.25z = 0.40 + 2.10
   $$  
   $$
   z = \frac{2.50}{0.25} = 10
   $$

3. **Calculate the year**:  
   Add $$ z = 10 $$ to the base year, 2004:  
   $$ 2004 + 10 = 2014 $$.

Thus, commodity X will cost 40 paise more than commodity Y in **2014**.

Answer

Answer

Answer