Let the required number of working hours per day be *x*.

*More pumps, Less working hours per day (Indirect Proportion)*

*Less days, More working hours per day (Indirect Proportion)*

Pumps | 4 | : | 3 | :: 8 : x | |

Days | 1 | : | 2 |

4 x 1 x *x* = 3 x 2 x 8

x = | (3 x 2 x 8) |

(4) |

*x* = 12.

Let the required number of bottles be *x*.

*More machines, More bottles (Direct Proportion)*

*More minutes, More bottles (Direct Proportion)*

Machines | 6 | : | 10 | :: 270 : x | |

Time (in minutes) | 1 | : | 4 |

6 x 1 x *x* = 10 x 4 x 270

x = | (10 x 4 x 270) |

(6) |

*x* = 1800.

Speed downstream = (13 + 4) km/hr = 17 km/hr.

Time taken to travel 68 km downstream = | 68 | hrs = 4 hrs. | |

17 |

Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.

Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.

(a) Since log_{a} *a* = 1, so log_{10} 10 = 1.

(b) log (2 + 3) = log 5 and log (2 x 3) = log 6 = log 2 + log 3

log (2 + 3) log (2 x 3)

(c) Since log_{a} 1 = 0, so log_{10} 1 = 0.

(d) log (1 + 2 + 3) = log 6 = log (1 x 2 x 3) = log 1 + log 2 + log 3.

So, (b) is incorrect.

log_{5} 512 |
| |||

| ||||

| ||||

| ||||

| ||||

| ||||

= 3.876 |

To obtain Rs. 10, investment = Rs. 96.

To obtain Rs. 650, investment = Rs. | 96 | x 650 | = Rs. 6240. | ||

10 |

Dividend on Rs. 20 = Rs. | 9 | x 20 | = Rs. | 9 | . | ||

100 | 5 |

Rs. 12 is an income on Rs. 100.

Rs. | 9 | is an income on Rs. | 100 | x | 9 | = Rs. 15. | ||

5 | 12 | 5 |

C.P. = Rs. 3000.

S.P. = Rs. | 3600 x 100 | = Rs. 3000. | ||

100 + (10 x 2) |

Gain = 0%.

Required money | = P.W. of Rs. 10028 due 9 months hence | |||||||||||

| ||||||||||||

= Rs. 9200. |