Let the required number of days be $ x $.
Less cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
$\therefore$ 1 x 40 x $ x $ = 40 x 1 x 40
$\Rightarrow x $ = 40.
Let the required number days be $ x $.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
$\therefore$ 1 x 7 x $ x $ = 7 x 1 x 7
$\Rightarrow x $ = 7.
Let the required number of bottles be $ x $.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
$\therefore$ 4 x 4 x $ x $ = 8 x 8 x 4
| $\Rightarrow x $ =$ \dfrac{(8 \times 8 \times 4)}{(4 \times 4)} $ |
$\Rightarrow x $ = 16.
Assume that initially garrison had provisions for $x$ men for $y$ days.
So, after 10 days, garrison had provisions for $x$ men for $(y-10)$ days
Also, after 10 days, garrison had provisions for $\dfrac{4x}{5}$ men for $y$ days $\left( ? x - \dfrac{x}{5} = \dfrac{4x}{5}\right)$
More men, Less days (Indirect Proportion)
(men) $x$ : $\dfrac{4x}{5}$ :: $y$ : $(y-10)$
$\Rightarrow x(y - 10) = \dfrac{4xy}{5}\\~\\$
$\Rightarrow (y - 10) = \dfrac{4y}{5}\\~\\$
$\Rightarrow 5(y - 10) = 4y\\~\\$
$\Rightarrow 5y - 50 = 4y \\~\\$
$\Rightarrow y = 50$
40 : x : : $\begin{cases}8 &: 30 ---(Men) \\12 &: 2 ---(Hectares) \end{cases}$
8 × 12 × x = 30 × 20 × 40
x = $\dfrac{30\times 20 \times 40}{8 \times 12}$ = 250 Hectares
We have to find the number of binders. Let the number of binders be x.
Direct Proportion:Less Books ($\downarrow$),Less binders($\downarrow$)
Indirect Proportion:More days ($\uparrow$),Less binders ($\downarrow$)
18 : x :: $\begin{cases}900 &: 600---(books) \\12 &: 10---(days) \end{cases}$
x × 900 × 12 = 18 × 600 × 10
x = $\dfrac{18\times 600 \times 10}{900 \times 12}$ = 10
Earlier time = 100 days.
Distance is doubled and speed is reduced to half.
∴ time will become 2 × 2 i.e. 4 times.
Hence now it will take 100 × 4 = 400 days.
Earlier dimensions of the wall = 100 × 3 × 0.30.
New dimensions = L × 1.5 × 0.3.
∴ As men, women and children are given to be equally efficient, so in the first case, the total number of persons is 100 (i.e. 30 + 20 + 50)
and the same in the second case is 75 (15 + 25 + 35).
Length of wall = L = (75x100) x (2x9) x (15x20) x (100 x 3 x 3 x 0.3)/(1.5 x 0.3) ⇒ L = 25 m.
Originally let there be x men.
Less men, More days (Indirect Proportion)
v
Therefore, (x-10) : x :: 100 :110
=> (x - 10) * 110 = x * 100 => x= 110
(2 x 14) men +(7 x 14) boys = (3 x 11) men + (8 x 11) boys
=>5 men= 10 boys => 1man= 2 boys
Therefore, (2 men+ 7 boys) = (2 x 2 +7) boys = 11 boys
( 8 men + 6 boys) = (8 x 2 +6) boys = 22 boys.
Let the required number of days be x.
More boys , Less days (Indirect proportion)
More work , More days (Direct proportion)
Boys22:11Work1 : 3}⋮⋮ 14:x
Therefore, (22 * 1 * x) = (11 * 3 * 14)
=> x = 21
Hence, the required number of days = 21