**1. Two friends A and B together can complete a piece of work in 10 days. In how many days A alone complete the piece of work?**

**Statement I :** B alone can complete half of the work in 12.5 days.

**Statement II :** The efficiency of A is 50% more than that of B.

A The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

B The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

C Either Statement I or Statement II alone is sufficient to answer the question.

D Neither statement I nor statement II is sufficient to answer the questions.

E The data in both the statements I and II together is necessary to answer the question.

**Correct Option: C**

**From the statement I, we can conclude the number of days A alone will take to complete the work. **

**From the statement II, efficiency is given so it is easy to find the number of days, A alone or B alone will take to complete the work. **

**Therefore, either Statement I or Statement II alone is sufficient to answer the question.**

**Hence, option C is correct.**

2. When length of a rectangle was increased by 20% and breadth remains constant then area was increased by 100 sq. cm. What is the perimeter of the rectangle.

**Statement I** : After increasing the length, the rectangle becomes a square.

**Statement II** : After increasing the length, all the angles of the rectangle becomes 90 degree.

A The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

B The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

C Either Statement I or Statement II alone is sufficient to answer the question.

D Neither statement I nor statement II is sufficient to answer the questions.

E The data in both the statements I and II together is necessary to answer the question.

**Correct Option: A**

**Let the length = x and breadth = y**

**When length was increased by 20% then the new length = 1.2x**

**From the statement I, we can conclude that 1.2x = y (because it changes to square)**

**x /y= 1/1.2 = 5/6**

**Let us assume that x = 5a then y = 6a**

**Original area = 5 × 6 × a2**

**New area = 5 × 5 × 1.2a2**

**From here we can conclude the value of a = 3 cm**

**Once we get the value of a, we can conclude the length and breadth and can get perimeter**

**From the Statement II, we could not conclude either new figure becomes rectangle or square because even in rectangle all angles are 90 degree.**

**Therefore, the data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.**

**Hence, option A is correct.**

**3. One day I left my home at 7 : 00 AM and assumed that if I run at uniform speed then I will reach my school at 12 : 00 AM. If my brother left the school for home at 8 : 00 AM with his uniform speed then at what time will he meet me?**

**Statement I :** The uniform speed of my brother is 14 km per hour.

**Statement II** : He can reach home at 11:30 AM.

A The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

B The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

C Either Statement I or Statement II alone is sufficient to answer the question.

D Neither statement I nor statement II is sufficient to answer the questions.

E The data in both the statements I and II together is necessary to answer the question.

**Correct Option: B**

**The time taken by me = 12 – 7 = 5 hours**

**From the statement I, speed of my brother = 14 km per hour**

**From the statement II, the time taken by my brother = 11: 30 – 8 : 00 = 3 : 30 hours**

**From the question and statement II, we can conclude the ratio of time = 5 : 3:30 = 10 : 7**

**Now we know that, speed = inversely proportional to time**

**So, the ratio of speed = 7 : 10**

**Let the distance between by house and the school is 70 km**

**Then my speed = 70/7 = 10 km per hour**

**And my brother speed = 70 /10= 7 km per hour**

**Now, we can conclude the time at which I will meet my brother but from the statement II, we could not conclude distance or any ratio.**

**Therefore, the data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.**

**Hence, option B is correct.**