Less weight, Less cost (Direct Proportion)
∴ 250 : 200 :: 60 : x ⟺ 250 x x = (200 x 60)
⟹ x= | (200 x 60) |
250 |
⟹ x = 48.
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.
Cost of 1 metre = Rs. | ❨ | d | ❩ |
x |
Cost of y metres = Rs. | ❨ | d | . y | ❩ | = Rs. | ❨ | yd | ❩. |
x | x |
Then, More cogs, Less revolutions (Indirect Proportion)
∴ 14 : 6 :: 21 : x ⟺ 14 x x = 6 x 21
⟹ x = | 6 x 21 |
14 |
⟹ x = 9.
Remaining meal is to be catered to 50 children.
Now, 200 children ≡ 120 men.
50 children ≡ | ❨ | 120 | x 50 | ❩ | = 30 men. |
200 |
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
Spiders | 1 | : | 7 | ] | :: 7 : x |
Webs | 7 | : | 1 |
∴ 1 x 7 x x = 7 x 1 x 7
⟹ x = 7.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
∴ 125 : 150 :: 35 : x ⟺ 125 x x = 150 x 35
⟹ x = | 150 x 35 |
125 |
⟹ x = 42.
Work done = | 5 |
8 |
Balance work = | ❨ | 1 - | 5 | ❩ | = | 3 |
8 | 8 |
Let the required number of days be x.
Then, | 5 | : | 3 | = :: 10 : x | ⟺ | 5 | x x = | 3 | x 10 |
8 | 8 | 8 | 8 |
⟹ x = | ❨ | 3 | x 10 x | 8 | ❩ |
8 | 5 |
⟹ x = 6.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons | 30 | : | 39 | ] | :: 12 : x |
Working hours/day | 6 | : | 5 |
∴ 30 x 6 x x = 39 x 5 x 12
⟹ x = | (39 x 5 x 12) |
(30 x 6) |
⟹ x = 13.
and 11¼ minutes as 675 seconds.
Rate upstream = | ❨ | 750 | ❩m/sec | = | 10 | m/sec. |
675 | 9 |
Rate downstream = | ❨ | 750 | ❩m/sec | = | 5 | m/sec. |
450 | 3 |
∴ Rate in still water = | 1 | ❨ | 10 | + | 5 | ❩m/sec |
2 | 9 | 3 |
= | 25 | m/sec |
18 |
= | ❨ | 25 | x | 18 | ❩km/hr |
18 | 5 |
= 5 km/hr.
Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.
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