A) 4:18 pm | B) 3:09 pm |

C) 12:15 pm | D) 11:09 am |

Explanation:

Efficiency of P= 100/20= 5% per hour

Efficiency of Q= 100/25= 4% per hour

Efficiency of R= 100/40= 2.5% per hour

Efficiency of S=100/50= 2% per hour

Cistern filled till 10 am by P, Q and R

$\left.\begin{array}{c}\mathrm{Till}10.00\mathrm{am}\mathrm{Pipe}\mathrm{P}\mathrm{filled}20\%\\ \mathrm{Till}10.00\mathrm{am}\mathrm{Pipe}\mathrm{Q}\mathrm{filled}8\%\\ \mathrm{Till}10.00\mathrm{am}\mathrm{Pipe}\mathrm{R}\mathrm{filled}2.5\%\end{array}\right\}30.5\%$

Thus, at 10 am pipe P,Q and R filled 30.5% of the cistern.

Rest of cistern to be filled = 100 - 30.5 = 69.5%

Now, the time taken by P,Q,R and S together to fill the remaining capacity of the cistern

= 69.5 / (5+4+2.5+2) = 5 Hours and 9 minutes(approx).

Therefore, total time =4 hrs + 5hrs 9 mins = 9 hrs and 9 mins

It means cistern will be filled up at 3:09 pm

A) 16 days | B) 72/5 days |

C) 15 days | D) 96/5 days |

Explanation:

Work done by Shyam and Rahim in 8 days **= 8/32 = 1/4**

Remaining work to be done by Shyam and Ram **= 1 - 1/4 = 3/4**

Given efficieny of Ram is half of Rahim i.e, as Rahim can do the work in 48 days, Ram can do the work in 24 days.

One day work of Ram and Shyam **= (1/32 - 1/48) + 1/24 = 5/96**

Hence, the total work can be done by Shyam and Ram together in **96/5 days.**

Therefore, remaining work 3/4 can be done by them in **3/4 x 96/5 = 72/5 = 14.4 days.**

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