More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
Wavers | 4 | : | 8 | ] | :: 4 : x |
Days | 4 | : | 8 |
∴ 4 x 4 x x = 8 x 8 x 4
⟹ x = | (8 x 8 x 4) |
(4 x 4) |
⟹ x = 16.
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.
Less men, More days (Indirect Proportion)
∴ 27 : 36 :: 18 : x ⟺ 27 x x = 36 x 18
⟹ x = | 36 x 18 |
27 |
⟹ x = 24.
Less cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
Cows | 1 | : | 40 | ] | :: 40 : x |
Bags | 40 | : | 1 |
∴ 1 x 40 x x = 40 x 1 x 40
⟹ x = 40.
If x = 3 + 2√2, then the value of | ❨ | √x | - | 1 | ❩ | is: |
√x |
❨ | √x | - | 1 | ❩ | 2 | = x + | 1 | - 2 |
√x | x |
= (3 + 2√2) + | 1 | - 2 |
(3 + 2√2) |
= (3 + 2√2) + | 1 | x | (3 - 2√2) | - 2 |
(3 + 2√2) | (3 - 2√2) |
= (3 + 2√2) + (3 - 2√2) - 2
= 4.
∴ | ❨ | √x | - | 1 | ❩ | = 2. |
√x |
Then, (17)3.5 + x = 178.
∴ 3.5 + x = 8
⟹ x = (8 - 3.5)
⟹ x = 4.5
Less lengthy shadow, Less in the height (Direct Proportion)
∴ 40.25 : 28.75 :: 17.5 : x ⟺ 40.25 x x = 28.75 x 17.5
x = | 28.75 x 17.5 |
40.25 |
⟹ x = 12.5
More metres, More time (Direct Proportion)
∴ 0.128 : 25 :: 1 : x ⟺ 0.128x = 25 x 1
x = | 25 | = | 25 x 1000 |
0.128 | 128 |
⟹ x = 195.31.
∴ Required time = 195 sec (approximately).
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.
Remaining meal is to be catered to 50 children.
Now, 200 children ≡ 120 men.
50 children ≡ | ❨ | 120 | x 50 | ❩ | = 30 men. |
200 |
Then, More cogs, Less revolutions (Indirect Proportion)
∴ 14 : 6 :: 21 : x ⟺ 14 x x = 6 x 21
⟹ x = | 6 x 21 |
14 |
⟹ x = 9.
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