**Directions : Study the following table chart carefully and answer the questions given below :**

**The villages of a district are classified into six categories, A through F, based on their population. The following table gives the number of villages in the district belonging to different categories in the years 2006 and 2016.**

Category |
Population |
No. of Villages in 2006 |
No. of Villages in 2016 |
Ratio of no. of male to female |
Number of Adults in population |
Literacy rate among adults × |

A |
< 200 |
104 |
92 |
5 : 3 |
60% |
60% |

B |
200 – 500 |
141 |
127 |
2 : 5 |
50% |
50% |

C |
501 – 1000 |
145 |
144 |
5 : 3 |
60% |
40% |

D |
1001 – 2000 |
110 |
129 |
3 : 2 |
60% |
40% |

E |
2001 – 5000 |
62 |
80 |
6 : 7 |
40% |
80% |

F |
> 5000 |
13 |
18 |
8 : 7 |
64% |
50% |

**The ratio of literacy for males to females in every category is the same as the ratio of the population of males to females given in the table**

**1 Find the population of category F village if 25% of adult female literate are doctors, 20% of rest adult female literate are engineers, 25% of rest of adult female literate are teachers and remaining 1008 of adult female literate are CA.**

A 12000

B 16000

C 20000

D 24000

E 30000

**Correct Option: D**

**Let there be 1000y adult literate females, then**

**0.75 × 0.8 × 0.75 × 1000y = 1008**

**y = 2.24**

**So, adult literate female = 2240**

**Now, total adult literate = (8 + 7)/7× 2240 = 4800**

**We have, 50% of Total adult (literate + illiterate) = 4800**

**So, Total adult (literate + illiterate) = 4800 × 2 = 9600**

**Then we have, 64% of Total population = number of adults (literate + illiterate) = 9600**

**Total Population = 100 × 9600/64 = 24000**

**Hence, option D is correct.**

**2 Find the average population of villages of category D in 2006 if there 15840 adult females are literate in category D from all the villages combined.**

A 1200

B 1500

C 1800

D 2000

E 2400

**Correct Option: B**

**Number of literate adults = 5/2 × 15840 = 39600**

**Number of adults (literate + illiterate) = 100 × 39600/40**

**Total population = 100/60 × ( 100 × 39600 )/40 = 165000**

**Average population of villages = 165000/110 = 1500**

**Hence, option B is correct.**

**3 In 2016, find the total population in category B villages was at least what percentage of the total population in category E villages?**

A 6.35%

B 6.75%

C 7.15%

D 7.25%

E 8.00%

**Correct Option: A**

**Here we have to take the least possible population of category B and the highest possible population of category E villages.**

**In 2016, least possible population of category B villages = 127 × 200**

**Highest possible population of category E villages = 80 × 5000**

**The percentage = 127 × 200 × 100 / (80 × 5000) = 6.35%**

**Hence, option A is correct.**

**4 If the total population in category D villages in 2016 was less than that in 2006, find what could be the least possible average population of category D villages in 2006? (approx)**

A 1165

B 1174

C 1192

D 1204

E 1222

**Correct Option: B**

**To find the least possible population of D in 2006, we must start with least possible population of D category villages in 2016.**

**So, Total Population of D type villages in 2016 = 1001 × 129**

**Since, it is less than what the population was in 2006, the population in 2006 must be in the form = 1001 × 129 + y, where y = 1, 2, 3, and so on.**

**But we have to tell the minimum possible population, we must choose y = 1.**

**So, total population in 2006 = 1001 × 129 + 1 = 129130**

**Average population = 129130/110 = 1173.9 = 1174 (approx)**

**Hence, option B is correct.**