Sister can bake 50 cakes in 25 hours. Sister and her mother together can bake 75 cakes in 15 hours. Based on this time and work information, how many cakes can the mother (Mummy) bake alone in 15 hours?

Introduction / Context:
This aptitude question tests the basic concept of work rate in time and work problems. We are given how many cakes the sister can bake alone and how many cakes sister and mother together can bake. From this data we have to find how many cakes the mother alone can bake in a given time period. Such questions are very common in competitive exams and help in understanding the relation between individual and combined efficiencies.

Given Data / Assumptions:
- Sister bakes 50 cakes in 25 hours.
- Sister and mother together bake 75 cakes in 15 hours.
- Work rate is assumed to be constant for each person.
- We are asked to find how many cakes the mother alone can bake in 15 hours.

Concept / Approach:
We use the standard time and work idea that work rate equals total work divided by total time. First we calculate the baking rate of the sister alone. Then we calculate the combined rate of sister and mother together. The difference between these two rates gives the mother's baking rate. Finally we use the mother's rate to compute how many cakes she can bake in 15 hours.

Step-by-Step Solution:
Step 1: Sister's rate = 50 cakes / 25 hours = 2 cakes per hour. Step 2: Combined rate of sister and mother = 75 cakes / 15 hours = 5 cakes per hour. Step 3: Mother's rate = combined rate − sister's rate = 5 − 2 = 3 cakes per hour. Step 4: Cakes baked by mother in 15 hours = 3 cakes per hour * 15 hours = 45 cakes. Step 5: Therefore the mother alone can bake 45 cakes in 15 hours.

Verification / Alternative check:
If mother bakes 3 cakes per hour and sister bakes 2 cakes per hour, then together they bake 5 cakes per hour. In 15 hours they would bake 5 * 15 = 75 cakes, which matches the given combined information. This confirms that the calculated individual rates for sister and mother are consistent with the problem statement and our final answer is correct.

Why Other Options Are Wrong:
Option 25: This would correspond to a mother's rate of less than 2 cakes per hour, which would make the combined rate less than 4 cakes per hour, not 5 cakes per hour.
Option 20: Gives an even smaller rate for the mother and cannot reach 75 cakes in 15 hours when combined with sister.
Option 10: This is far too low, as then the mother would bake less than 1 cake per hour and the combined rate would not match the given data.

Common Pitfalls:
A frequent mistake is to directly average the numbers of cakes or times without using rates. Another mistake is to forget that the combined rate is the sum of individual rates, not the average. Some learners also confuse total cakes with rate per hour. Always convert to rates first and then solve systematically.

Final Answer:
The mother can bake 45 cakes in 15 hours working alone.