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 loga a = 1, so log10 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 loga 1 = 0, so log10 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.
log5 512 |
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= 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 | |||||||||||
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= Rs. 9200. |