Final answer:
The cost price of A increases to 105 units after two consecutive increases of 40% and 25%, while the cost price of B decreases to 80 units after a reduction of 20%. Comparing the new prices, the value of A increases by approximately 31.25% relative to the new cost price of B, with the closest given option being 25%. The correct answer is d. 25%.
Step-by-step explanation:
To solve the problem, we need to understand the percentage changes and the resulting values for the cost prices of A and B. Let's define the initial cost price of B as 100 units since we don't have a specific value. Consequently, the cost price of A is then 60 units because A costs 40% less than B.
Now, if A's cost price is increased by 40% and then by another 25%, we perform the following calculations:
First increase: 60 + (40/100 * 60) = 84 units.
Second increase: 84 + (25/100 * 84) = 105 units.
Therefore, the final cost price of A after both increases is 105 units.
Let's look at B now, whose cost is reduced by 20%. Hence:
New cost price of B: 100 - (20/100 * 100) = 80 units.
Comparing the new cost price of A to the reduced cost price of B: A is now 105 units, and B is 80 units. To find the increase of A in percent relative to the new cost price of B, we calculate:
(105 - 80) / 80 * 100 = 31.25%.
Using this method, we find that option d. 25% is the closest to our result, even though it is not exact. Therefore, the value of A in % increases compared to the reduced cost price of B is slightly greater than 25%.