Following

**1. The total number of boy students enrolled in Dancing and Singing together is approximate what percentage of the total number of girl students enrolled for the same activities?**

**Answer**: Option C

**Explanation**:

Total number of students enrolled for Dancing = 2500 × (\(\frac{18}{100}\)) = 450

Total number of students enrolled for Singing = 2500 × (\(\frac{14}{100}\)) = 350

Total number of girl students enrolled for Dancing =1200 × (\(\frac{21}{100}\)) = 252

Total number of girl students enrolled for Singing = 1200 × (\(\frac{12}{100}\)) = 144

Total number of boy students enrolled for Dancing = 450 – 252 = 198

Total number of boy students enrolled for Singing = 350 – 144 = 206

Required % = \(\frac{198 + 206}{252 + 144}\) × 100

= > (\(\frac{404}{396}\)) × 100 = 102.02 % = 102 %

**2. Find the difference between the total number of students enrolled for Drawing and Karate together to that of total number of girl students enrolled for Karate and Swimming together?**

**Answer**: Option B

**Explanation**:

The total number of students enrolled for Drawing and Karathe together

= > 2500 × (\(\frac{52}{100}\)) = 1300

The total number of girl students enrolled for Karathe and Swimming together

= > 1200 × (\(\frac{50}{100}\)) = 600

Required difference = 1300 – 600 = 700

**3. Find the ratio between the total number of boy students enrolled for Dancing and Swimming together to that of total number of girl students enrolled for Drawing and Karate together?**

**Answer**: Option D

**Explanation**:

Total number of students enrolled for Dancing = 2500 × (\(\frac{18}{100}\)) = 450

Total number of girl students enrolled for Dancing =1200 × (\(\frac{21}{100}\)) = 252

Total number of boy students enrolled for Dancing = 450 – 252 = 198

Total number of students enrolled for Swimming = 2500 × (\(\frac{16}{100}\)) = 400

Total number of girl students enrolled for Swimming = 1200 × (\(\frac{23}{100}\)) = 276

Total number of boy students enrolled for Swimming = 400 – 276 = 124

The total number of boy students enrolled for Dancing and Swimming together

= > 198 + 124 = 322

The total number of girl students enrolled for Drawing and Karathe together

= > 1200 × (\(\frac{44}{100}\)) = 528

Required ratio = 322 : 528 = 161 : 264

**4. Find the average number of boy students enrolled for Singing, Drawing, and Karate together?**

**Answer**: Option A

**Explanation**:

Total number of students enrolled for Singing = 2500 × (\(\frac{14}{100}\)) = 350

Total number of girl students enrolled for Singing= 1200 × (\(\frac{12}{100}\)) = 144

Total number of boy students enrolled for Singing = 350 – 144 = 206

Total number of students enrolled for Drawing = 2500 × (\(\frac{24}{100}\)) = 600

Total number of girl students enrolled for Drawing = 1200 × (\(\frac{17}{100}\)) = 204

Total number of boy students enrolled for Drawing = 600 – 204 = 396

Total number of students enrolled for Karathe = 2500 × (\(\frac{28}{100}\)) = 700

Total number of girl students enrolled for Karathe = 1200 × (\(\frac{27}{100}\)) = 324

Total number of boy students enrolled for Karathe = 700 – 324 = 376

Total number of boy students enrolled for Singing, Drawing and Karathe together

= > 206 + 396 + 376 = 978

Required average = \(\frac{978}{3}\) = 326

**5. The total number of students enrolled for Singing and Swimming together is approximately what percentage more/less than the total number of girl students enrolled for Dancing, Drawing and Karate together?**

**Answer**: Option C

**Explanation**:

Total number of students enrolled for Singing and Swimming together

= > 2500 × (\(\frac{30}{100}\)) = 750

Total number of girl students enrolled for Dancing, Drawing and Karathe together

= > 1200 × (\(\frac{65}{100}\)) = 780

Required % = \(\frac{(780 – 750)}{780}\) × 100 = \(\frac{30}{780}\) × 100 = 4 % less

There are two companies namely A and B, which sell chairs, tables, and wardrobes in 3 months August, September, and October. The ratio of a chair, tables, and wardrobes sold by A in August are 42: 36: 23 while a ratio of chairs sold by A in August, September, and October is 14: 23: 27. Wardrobes sold by A in August is 230 less than chairs sold in September by A. In September 665 chairs, 400 tables and 210 wardrobes were sold by two companies together. B sold the same number of chairs in Aug and September. The number of tablets sold by company B in September was equal to a number of chairs sold by A in August while the number of wardrobes sold by A in August and B in September was equal. Company B sold a total of 1025 chairs in these three months together which was 480 more than the total number of tables sold by A. Ratio of tables sold by A and B in August is 12: 11 and in October is 35: 38 respectively. The total number of items sold in August was 1075. The total number of wardrobes sold by A in October was 35 less than the wardrobe sold by B in October, while the sum of the wardrobe

sold by A and B in October is 205.

**1. What is the ratio of the number of tables sold by A in August to that of B in September?**

**Answer**: Option B

**Explanation**:

Let number of chairs, tables and wardrobes sold by A in August be 42x, 36x and 23x. Also, let chairs sold by A in August, September and October be 14y,

23y and 27y respectively.

∴42x = 14y ⇒y = 3x

and, 23x = 23y – 230

⇒x = 5 and y = 15

Now,

Chairs sold by B in September = 665 – 345 = 320

Chairs sold by B in August = 320

Tables sold by B in September = Chairs sold by A in Aug = 210

∴Table sold by A in September = 400 – 210 = 190

Wardrobes sold by B in September = wardrobes sold by A in Aug = 115

∴Wardrobes sold by A in September = 210 – 115 = 95

Chairs sold by B in October = 1025 – 320 – 320 = 385

Tables sold by A in October = (1025 – 480) – (180 + 190) = 175

Tables sold by B in August = (\(\frac{11}{12}\)) × 180 = 165

Tables sold by B in October = (\(\frac{38}{35}\)) × 175 = 190

Wardrobes sold by B in August = 1075 – (210 + 320 + 180 + 165 + 115) = 85

Let wardrobes sold by A in October be a and that by B be b in October

∴a = b – 35 and a + b = 205

⇒a = 85 and b = 120

Month | chair | Table | wardrobe | |||
---|---|---|---|---|---|---|

A | B | A | B | A | B | |

Aug | 210 | 320 | 180 | 165 | 115 | 85 |

Sep | 345 | 320 | 190 | 210 | 95 | 115 |

Oct | 405 | 385 | 175 | 190 | 85 | 120 |

Required Ratio = \(\frac{180}{120}\) = \(\frac{6}{7}\)

**2. Find the number of wardrobes sold by B in October.**

**Answer**: Option B

**Explanation**:

Refer to the table in Explation of Q1, Wardrobes sold by B in Oct = 120

**3. Find the difference in the number of chairs sold by A and B in August.**

**Answer**: Option D

**Explanation**:

Refer to the table in Explation of Q1, Required difference = 320 – 210 = 110

**4. Total number of chairs sold by B in September and October is**

**Answer**: Option C

**Explanation**:

Refer to the table in Explation of Q1, Total chairs sold by B in September and October = 320 + 385 = 705

**5. By what percent tables sold by A in October are more than wardrobes sold by B in October?**

**Answer**: Option A

**Explanation**:

Refer to the table in Explation of Q1, [ \(\frac{(175-120)}{120}\)] × 100 = 45.83%

Villlages | 2001 | 2005 |
---|---|---|

A | 50 | 80 |

B | 75 | 65 |

C | 76 | 64 |

D | 55 | 70 |

E | 80 | 55 |

**NOTE**– Total voters in any year = Valid voters + Invalid voters

**1. What is the difference between invalid voters of village C in the two given years if valid voters in 2005 in that village are 4000 and the ratio of valid voters of village C from 2001 to 2005 is 19: 25?**

**Answer**: Option C

**Explanation**:

Invalid voter of village C in 2005 = 4000 × \(\frac{36}{64}\) = 2250

Valid voter of village C in 2001 = 4000 × \(\frac{19}{25}\) = 3040

Now, invalid voter of village C in 2001 = 3040 × \(\frac{24}{76}\) = 960

∴Required diff. = 2250 – 960 = 1290

**2. If in village A in 2005, 2500 voters were declared invalid voters 10% of valid voters opted NOTA and the winner got 200 more votes than losing candidate, then find the total vote that losing candidate got in 2005 in village A.**

**Answer**: Option A

**Explanation**:

Total valid votes of village A in 2005 = 2500 × \(\frac{100}{20}\) × \(\frac{80}{100}\) = 10000

Total valid votes excluding Nota in village A in 2005 = 10000 × \(\frac{90}{100}\) = 9000

∴According to question,

x + (x + 200) = 9000

⇒ x = 4400

Required no. of votes of losing candidates = 4400

**3. In village B if the ratio of total voters in 2001 to 2005 is 26: 23, then find the ratio of invalid voters in 2001 to the invalid voters in 2005 in same village.**

**Answer**: Option B

**Explanation**:

Let the total voters in 2005 are x.

Total voters in 2001 = (\(\frac{26}{23}\)) x

∴ \(\frac{\frac {75}{100} × \frac{30}{100} × x }{\frac{30}{100} × x }\) = \(\frac{130}{161}\)

**4. If there are 1600 males invalid voters of village E in 2001 and the females’ invalid voters of the same village and same year contributed is 36% of total valid voters, then find the percentage of invalid male voters in a total population if total males in village E in 2001 were 2000.**

**Answer**: Option D

**Explanation**:

Total invalid male of village E in 2001

= 2000 – 1600 = 400

Total valid voters in 2001 = 1600 × \(\frac{100}{64}\) = 2500

Total Voters in 2001 = 2500 × \(\frac{100}{80}\) = 3125

∴ required % = (\(\frac{400}{3125}\)) × 100 = 12.8 %

**5. If the ratio of valid voters of village B in 2001 and invalid voters of village D in 2005 was 16: 3, then total voters of village D in 2005 were what percent more or less than those of village B in 2001?**

**Answer**: Option C

**Explanation**:

Let total voters of village B in 2001 = x

& Total voters of village D in 2005 = y \(\frac{\frac{20x}{3}}{80}\)

∴ [ \(\frac{\frac {75}{100} × x}{\frac{30}{100} × y}\) ] = \(\frac{16}{3}\)

\(\frac{x}{y}\) = \(\frac{32}{15}\)

Required % = \(\frac{17}{32}\) × 100 = 53 \(\frac{1}{8}\) %