### Directions: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer.

**1. What is the value of the two-digit number?**

**Statement I :** The sum of the digits at unit’s place and tenth’s place is 13.

**Statement II :** When the digits are interchanged then the number obtained is 45 larger than the original number.

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 The data in both the statements I and II is not sufficient to answer the question.

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

**E**

**Let the two-digit number = ab = 10a + b**

**From the statement, I, we can conclude that, a + b = 13 **

**From the statement II, we can conclude that, 10b + a = 10a + b + 45 **

**9(b – a) = 45 **

**If we solve the both the equation then we can get our answer as 49 **

**Therefore, the data in both the statements I and II together is necessary to answer the question**

**Hence, option E is correct.**

### 2. Can a water tank of 2500 litres capacity be filled by two inlet pipes A and B together in less than 8 hours?

### Statement I : If pipe A is opened alone then it takes 12 hours to fill the tank.

### Statement II : Pipe B can fill 1 litres of water per minute.

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 The data in both the statements I and II is not sufficient to answer the question.

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

**Correct Option: E**

**From the statement I, the efficiency of pipe A per hour**

**= 2500/12 = 625/3 litres per hour**

**From the statement II, the efficiency of pipe B = 1 × 60 = 60 litres per hour**

**Pipe A and B together will fill in 1 hour**

**= 625/3 + 60 = 805/3 litres per hour**

**The time it will take to fill 2500 litres of water = more than 8 hours, therefore the answer will be no**

**Therefore, the data in both the statements I and II together are necessary to answer the question**

**Hence, option E is correct.**

**3. How much time will Ram take to cover a distance of 100 km at a uniform speed?**

**Statement I : The speed of Mohan is 10 km per hour more than that of Ram.**

**Statement II : If Mohan increases his speed by 25% then he takes 3 hours 20 minutes less to cover a distance of 500 km.**

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 The data in both the statements I and II is not sufficient to answer the question.

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

**Correct Option: E**

**Let the speed of ram = x km per hour **

**Then the speed of Mohan = y km per hour **

**From the statement I, y = x + 10 **

**From the statement II, we can find the value of y as 30 , so speed of Mohan is 30 km per hour**

**By combining both the statement, we can get the value of x as well which is 20 km per hour**

**So Ram will take 5 hours to cover 100km at a speed of 20 km per hour**

**Hence, option E is correct.**

**4. What is the sum of x and y?**

**Statement I : 15x + 4y = 108**

**Statement II : y = 27 – 3.75x**

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.

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

D The data in both the statements I and II is not sufficient to answer the question.

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

**Correct Option: D**

**From the statement I, 15x + 4y = 108 —– (i)**

**From the statement II, y = 27 – 3.75x**

**4y + 15x = 108 —– (ii)**

**Here, both the equations are same it means we have two variable and one equation therefore we could not conclude the value of two variable from one equation.**

**Therefore, the data in both the statements I and II is not sufficient to answer the question.**

**Hence, option D is correct.**