**1. Pranav and Pankaj started working together. After a few days, Prashant joined them and they were able to finish the work in 10 days. All of them together were paid a total of Rs. 800. Find the share of Prashant.**

**Statement I :** Pranav can do the work in 20 days, while Pankaj can do the same work in 25 days.

**Statement II :** Pranav can do the work in 60 days, while Pankaj can do the same work in 15 days.

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

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

C If the data either in statement I alone or in statement II alone is sufficient to answer the question

D If the data in both statements I and II together are necessary to answer the question

E If the data given in both statements I and II together are not sufficient to answer the question.

**Correct Option: C**

**From statement I:**

**In 1 day, Pranav finishes 1/20th of the work.**

**In 1 day, Pankaj finishes 1/25th of the work.**

**The work was completed in 10 days.**

**Part of work completed by Pranav and Pankaj in 10 days**

**= 10 ( 1/20 + 1/25 ) = 9/10**

**Part of work completed by Prashant = 1 – 9/10 = 1/10**

**Amount received as payment will be proportional to the amount of work done.**

**Amount paid to Prashant = 800 × 1/10 = Rs. 80**

**Similarly, from statement II we also can find the share of Prashant.**

**∴ Either of the statements alone is sufficient to answer this question.**

**Hence, option C is correct.**

**2. Two partners, P and Q entered in a business, what profit will Q get at the end of 2 years? **

**Statement I :** P and Q started the business by investing in the ratio 4: 7 and After 2 years, P’s share is Rs. 95000.

**Statement II :** P joined the business with an amount of Rs. 500000

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

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

C If the data either in statement I alone or in statement II alone is sufficient to answer the question

D If the data in both statements I and II together are necessary to answer the question

E If the data given in both statements I and II together are not sufficient to answer the question.

**Correct Option: A**

**From statement I:**

**Share of profit of P and Q will be in the ratio of 4 : 7**

**After two years,**

**Let the share of profit of Q be Rs. y**

**∴ 4/7 = 95000/y**

**⇒ y = 95000 × 7/4**

**⇒ y = Rs. 166250**

**∴ Statement I alone is sufficient to answer.**

**From statement II: Only P’s investment is given so we can’t find the profit of Q.**

**Hence, option A is correct.**

**3. Find the total population of Kanpur.**

**Statement I** : The ratio of the population of males and females in Kanpur is 33 : 29 and the difference between their population is 24000.

**Statement II :** The population of Kanpur is 60% of that of Patna, and the difference between the population of Kanpur and Patna is 35000.

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

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

C If the data either in statement I alone or in statement II alone is sufficient to answer the question

D If the data in both statements I and II together are necessary to answer the question

E If the data given in both statements I and II together are not sufficient to answer the question.

**Correct Option: C**

**From statement I: **

**Let the total population of Kanpur be X.**

**⇒ 32X – 29X = 24000 **

**⇒ 4X = 24000 **

**⇒ X = 6000 **

**∴ The total population 33X + 29X = 62X **

**62X = 62 × 6000 = 372000**

**From statement II: **

**Let the total population of Kanpur be X.**

**So, population of Patna = 100X/60 = 5X/3**

**∴ 5X/3 – X = 35000**

**⇒ 2X = 105000 **

**⇒ X = 52500 **

**∴ Statement I or II alone is sufficient to answer the question.**

**Hence, option C is correct.**