A) 15 | B) 30 |

C) 25 | D) 10 |

Explanation:

Combined efficiency of all the three boats = 60 passenger/trip

Now, consider option(a)

15 trips and 150 passengers means efficiency of B1 = 10 passenger/trip

which means in carrying 50 passengers B1 must has taken 5 trips. So the rest trips equal to 5 (10-5 = 5) in which B2 and B3 together carried remaining 250 (300 - 50 = 250) Passengers.

Therefore the efficiency of B2 and B3 = 250/5 = 50 passenger/trip

Since, the combined efficiency of B1, B2 and B3 is 60. Which is same as given in the first statement hence option(a) is correct.

A) 38 | B) 72 |

C) 36 | D) 76 |

Explanation:

Given 4men, 12 women and 20 children work for 2 days.

Workdone for 2 days by 4men, 12 women and 20 children = $\frac{\mathbf{4}\mathbf{}\mathbf{x}\mathbf{}\mathbf{2}}{\mathbf{6}\mathbf{}\mathbf{x}\mathbf{}\mathbf{12}}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{12}\mathbf{}\mathbf{x}\mathbf{}\mathbf{2}}{\mathbf{8}\mathbf{}\mathbf{x}\mathbf{}\mathbf{18}}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{20}\mathbf{}\mathbf{x}\mathbf{}\mathbf{2}}{\mathbf{18}\mathbf{}\mathbf{x}\mathbf{}\mathbf{10}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1}}{\mathbf{2}}$

Therefore, remaining work = 1 - $\frac{1}{2}$ = $\frac{1}{2}$

To complete the same work by only men in 1 day,

We know that M1 x D1 = M2 x D2

Here M1 = 6 , D1 = 12 and M2 = M , D2 = 1

12 x 6 = M x 1

=> M = 12 x 6 = 72

=> But the remaining work = 1/2

Men required => 1/2 x 72 = 36

Only men required to Complete the remaining work in 1 day = 36.

A) 7 | B) 8 |

C) 9 | D) 6 |

Explanation:

Given (3 Men + 4 Women + 6 Children) -----> 9 days

But W = 2M and C = M/2

Now, convert Men and Children into Women by

$\mathbf{3}\frac{\mathbf{W}}{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{4}\mathbf{W}\mathbf{}\mathbf{+}\mathbf{}\mathbf{6}\frac{\mathbf{W}}{\mathbf{4}}\phantom{\rule{0ex}{0ex}}\mathbf{=}\mathbf{}\mathbf{}\frac{\mathbf{3}}{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{4}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{3}}{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{7}\mathbf{}\mathbf{Women}$

Therefore, * 7 women *alone can complete this work in 9 days.

A) 35/4 days | B) 17.5 days |

C) 19 3/4 days | D) 37/3 days |

Explanation:

Let the number of days be 'p'

As the work is same, we know that

$\mathbf{M}\mathbf{1}\mathbf{}\mathbf{x}\mathbf{}\mathbf{D}\mathbf{1}\mathbf{}\mathbf{x}\mathbf{}\mathbf{H}\mathbf{1}\mathbf{}\mathbf{=}\mathbf{}\mathbf{M}\mathbf{2}\mathbf{}\mathbf{x}\mathbf{}\mathbf{D}\mathbf{2}\mathbf{}\mathbf{x}\mathbf{}\mathbf{H}\mathbf{2}$

Where M = Men, D = Days, H = Hours per day

Here M1 = 9, D1 = 15, H1 = 7

M2 = 6, D2 = p, H2 = 9

=> 9 x 15 x 7 = 6 x p x 9

=> p = 35/2 = 17.5 days.

A) 45 | B) 44 |

C) 46 | D) 47 |

Explanation:

Here given soldier shots 7 shots in 12 min

=> 1 shot doen't take any time in 12 min

=> Only 6 shots take 12 min

12 min ------ 6 shots

90 min ------ ? shots

=> 90 x (6/12) = 45

Therefore, total shots fired in 90 minutes = 45 + 1 = 46 shots.

A) 111 | B) 117 |

C) 123 | D) 139 |

Explanation:

We know that, $\frac{\mathbf{M}\mathbf{1}\mathbf{}\mathbf{\times}\mathbf{}\mathbf{D}\mathbf{1}}{\mathbf{W}\mathbf{1}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{M}\mathbf{2}\mathbf{}\mathbf{\times}\mathbf{}\mathbf{D}\mathbf{2}}{\mathbf{W}\mathbf{2}}$

Here M1 = 1, D1 = 6 min, W1 = 1 and M2 = M, D2 = 90 min, W2 = 1845

$\frac{\mathbf{1}\mathbf{}\mathbf{\times}\mathbf{}\mathbf{6}}{\mathbf{1}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{M}\mathbf{}\mathbf{\times}\mathbf{}\mathbf{90}}{\mathbf{1845}}$

=> **M = 123**

A) 4 days | B) 6 days |

C) 7 days | D) 5 days |

Explanation:

Given that

6 men and 8 boys can do a piece of work in 10 days

26 men and 48 boys can do the same in 2 days

As the work done is equal,

10(6M + 8B) = 2(26M + 48B)

60M + 80B = 52M + 96B

=> M = 2B

=> B = M/2 ……(1)

Now Put (1) in 15M + 20B

=> 15M + 10M = 25M

Now, 6M + 8B in 10 days

=> (6M + 4M) 10 = 100M

Then D(25M) = 100M

=> D = 4 days.

A) 36 | B) 32 |

C) 22 | D) 28 |

Explanation:

Let the total women in the group be **'W'**

Then according to the given data,

**W x 20 = (W-12) x 32**

=> W = 32

*Therefore, the total number of women in the group =* 32

A) 16 days | B) 13 days |

C) 15 days | D) 12 days |

Explanation:

Ratio of times taken by P & Q = 100 : 130 = 10:13

Let Q takes x days to do the work

Then, 10:13 :: 23:x

=> x = 23x13/10

=> x = 299/10

P's 1 day's work = 1/23

Q's 1 day's work = 10/299

(P+Q)'s 1 day's work = (1/23 + 10/299) = 23/299 = 1/13

Hence, P & Q together can complete the work in **13** days.