Mains exams are very important to clear every

**Answer**: Option A

**Explanation**: 40% of 375 ÷ \(\sqrt[3]{512}\)× 30 = 4500 ÷ ?

150 ÷ 8 × 30 = 4500 ÷ ?

? = 4500 × 8 ÷ 150 ÷ 30

? = 8

**2. What should come at the place of Question mark (?) in the following question?**

\({?}{^3}\) – 300 – 43 + 4 = 148 ÷ 37

**Answer**: Option B

**Explanation**: \({?}{^3}\) – 300 – 43 + 4 = 148 ÷ 37

\({?}^{3}\) – 343 + 4 = 4

\({?}^{3}\) = 343

? = 7

**3. What should come at the place of Question mark (?) in the following question?**

299 ÷ \(\sqrt{169}\) x 11 – \(\sqrt{361}\) = \({?}^{2}\) + 38

**Answer**: Option D

**Explanation**: \(\frac{299}{\sqrt{169}}\) x 11 – \(\sqrt{361}\) = \({?}^{2}\) + 38

\(\frac{299}{13}\) x 11 – 19 – 38 = \({?}^{2}\)

253 – 57 = \({?}^{2}\)

\({?}^{2}\) = 196

? = 14

**4.What should come at the place of Question mark (?) in the following question?**

42.5% of 750 = ?% of 43 – 26% of ?

**Answer**: Option D

**Explanation**: From I, total sale of product A = Rs. (8000 x 25) = Rs. 200000.42.5% of 750 = ?% of 43 – 26% of ?

85% of 375 = \(\frac{43 × ? – 26 × ?}{100}\)

85% of 375 = 17 x \(\frac{?}{100}\)

85 × \(\frac{375}{17}\) = ?

5 × 375 = ?

? = 1875

**5. What should come at the place of Question mark (?) in the following question?**

2\(\frac{11}{13}\) – 3\(\frac{1}{13}\) + 5\(\frac{1}{4}\) = ? × 87

**Answer**: Option C

**Explanation**:2\(\frac{11}{13}\) – 3\(\frac{1}{13}\) + 5\(\frac{1}{4}\) = ? × 87

(2 – 3 + 5) + \(\frac{11}{13}\) – \(\frac{1}{13}\) + \(\frac{1}{4}\) = ? x 87

4 + \(\frac{44 – 4 + 13 }{52}\) = ? × 87

4 + \(\frac{53}{52}\) = ? × 87

\(\frac{261}{52}\) = ? × 87

\(\frac{261}{52 × 87}\) = ?

? = \(\frac{3}{52 }\)

**Answer**: Option C

**Explanation**:

Series Pattern | Given Pattern |
---|---|

24 | 24 |

24 x \(\frac{1}{2}\) = 12 | 12 |

12 × 1 = 12 | 12 |

12 x \(\frac{3}{2}\) = 18 | 18 |

18 x 2 = 36 | 36 |

36 x \(\frac{5}{2}\) = 90 | 90 |

**2. 13, 19, 30, 48, 75, ?**

**Answer**: Option D

**Explanation**:

Series Pattern | Given Pattern |
---|---|

13 | 13 |

13 + (3 + 3) = 19 | 19 |

19 + (6 + 5) = 30 | 30 |

30 + (11 + 7) = 48 | 48 |

48 + (18 + 9) = 75 | 75 |

75 + (27 + 11) = 113 | 113 |

**3. 2, 8, 26, ?, 242**

**Answer**: Option D

**Explanation**:

Series Pattern | Given Pattern |
---|---|

2 | 2 |

2 × 3 + 2 = 8 | 8 |

8 × 3 + 2 = 26 | 26 |

26 × 3 + 2 = 80 | 30 |

**4. 7, 13, ?, 49, 97**

**Answer**: Option B

**Explanation**:

Series Pattern | Given Pattern |
---|---|

7 | 7 |

7 × 2 – 1 = 13 | 13 |

13 × 2 – 1 = 25 | 25 |

25 × 2 – 1 = 49 | 49 |

49 × 2 – 1 = 97 | 97 |

**5. 5, 16, 49, 104, ?, 280**

**Answer**: Option D

**Explanation**:

Series Pattern | Given Pattern |
---|---|

5 | 5 |

5 + (11 × 1) = 16 | 16 |

16 + (11 × 3) = 49 | 49 |

49 + (11 × 5) = 104 | 104 |

104 + (11 × 7) = 181 | 181 |

181 + (11 × 9) = 280 | 1 |

**Answer**: Option B

**Explanation**: Let 1 day’s efficiency of each of the individuals is A, B and C respectively.

As per the given information, we get the efficiency equations as follows

3A = (B + C) …(i)

A + B + C = 24 …..(ii)

Putting 3A in place of (B + C) in equation (ii), we get

A + 3A = 24

4A = 24

Now, 4A do the whole work in 24 days.

Therefore, A alone will do the whole work in 24 × 4 = 96 days

**2. 4 boys and 3 women can do a piece of work in 6 days while 2 boys and 4 women can do the same piece of work in 9 days. How much time will be taken by 7 boys and 9 women to do the same piece of work?**

**Answer**: Option A

**Explanation**: As per the given information, work done by 4 boys and 3 women in 6 days must be equal to work done by 2 boys and 4 women in 9 days.

Therefore, we get

(4B + 3W) × 6 = (2B + 4W) × 9

⇒ 24B + 18W = 18B + 36W

⇒ 6B = 18W ⇒ 1B = 3W

Now, 2B + 4W= (2 × 3)W + 4W = 10W

⇒ 10 women do a piece of work in 9 days.

Similarly, 7B + 9W = (7 × 3)w + 9W = 30W

Now, when 10 women do a piece of work in 9 days,

30 women (thrice of 10) will do the same piece of work in 3 days (∵ Time ∝ 1/Efficiency ).

**3. Working alone, Typewriters A, B, C can do a certain typing job, consisting of a large number of pages, in 12, 15 and 18 hours, respectively. What is the ratio of the time it takes Typewriter A to do the job, working alone at its rate, to the time it takes Type writer B and C to do the job, working together at their individual rate?**

**Answer**: Option D

**Explanation**: Since Typewriter B can do the job in 15 hours, it can do \(\frac{1}{15}\) of the job in 1 hour.

Since Typewriter C can do the job in 18 hours

it can do \(\frac{1}{18}\) of the job in 1 hour.

Together Typewriters B and C can do = (\(\frac{1}{15}\) + \(\frac{1}{18}\)) = \(\frac{6}{90}\) + \(\frac{5}{90}\) = \(\frac{11}{90}\) of the job in 1 hour

Which means that it takes them = \(\frac{11}{90}\) hours

to complete the job. Since Typewriter A completes the job in 12 hours, the ratio of the time required for A to do the job to the time required for B and C working together to do the job is

\(\frac{12}{\frac{90}{11}}\) = \(\frac{12(90)}{11}\) = \(\frac{2(11)}{15}\) = \(\frac{22}{15}\)

**4. A, B and C can do a piece of work in 4, 7 and 8 days respectively. They undertook to finish the work together for Rs. 53650. Find the difference (in Rs.) between the share of A and that of B**

**Answer**: Option B

**Explanation**: The ratio of shares of A, B and C = The \(\frac{1}{4}\):\(\frac{1}{7}\): \(\frac{1}{8}\)

= \(\frac{14}{56}\):\(\frac{8}{56}\): \(\frac{7}{56}\)= 14 : 8 : 7

Difference between the shares of A and B in ratio = \(\frac{6}{29}\)

∴ Actual difference in value = \(\frac{6}{29}\)× 53650 = 11,100/-

**5. P is thrice as good a workman as Q and together they finish a piece of work in 24 days. The number of days taken by P alone to finish the work is:**

**Answer**: Option C

**Explanation**: P’s 1 days’ work) : (Q’s 1 days’ work) = 3 : 1

(P + Q)’s = 1 days work = \(\frac{1}{24}\)

Divide \(\frac{1}{24}\) in the ratio 3 : 1

P’s 1 day’s work = [\(\frac{1}{24}\) x \(\frac{3}{4}\)]⇒ \(\frac{1}{32}\)

Hence, P alone can finish the work in 32 days.

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