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)
$\therefore$ 4 x 1 x $ x $ = 3 x 2 x 8
| $\Rightarrow x $ =$ \dfrac{(3 \times 2 \times 8)}{(4)} $ |
$\Rightarrow x $ = 12.
Cost of $ x $ metres = Rs. d.
Cost of 1 metre = Rs.$ \left(\dfrac{d}{x} \right) $
Cost of $ y $ metres =$\left(\dfrac{d}{x}.y\right)$=Rs $\left(\dfrac{yd}{x}\right)$
Let the required number of bottles be $ x $.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
$ \begin{cases}6 : 10\\1 : 4 \end{cases}::270:x$
$\therefore$ 6 x 1 x $ x $ = 10 x 4 x 270
| $\Rightarrow x $ =$ \dfrac{(10 \times 4 \times 270)}{(6)} $ |
$\Rightarrow x $ = 1800.
After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for $ x $ days.
Now, Less men, More days (Indirect Proportion)
$\therefore$ 125 : 150 :: 35 : $ x $ $\Leftrightarrow$ 125 x $ x $ = 150 x 35
| $\Rightarrow x $ =$ \dfrac{150 \times 35}{125} $ |
$\Rightarrow x $ = 42.
Let the required number of days be $ x $.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
$\therefore$ 30 x 6 x $ x $ = 39 x 5 x 12
| $\Rightarrow x $ =$ \dfrac{(39 \times 5 \times 12)}{(30 \times 6)} $ |
$\Rightarrow x $ = 13.
Men = M; Days = D; Time/Hours = T; Work = W
M1D1T1W2 = M2D2T2W1
Note that - W2 is on left side and W1 is on right side
∴ 20 women x 20 minutes x ? = 400 women x 400 minutes x 20 chapattis
∴ ? = 8000 chapattis = Are rolled by 400 women in 400 minutes
Men = M; Days = D; Time/Hours = T; Work = W
M1D1T1W2 = M2D2T2W1
Note that - W2 is on left side and W1 is on right side
Take work done = 1
∴ 40 men x 96 days x 9 hours x 1 = 48 men x 45 days x ? hours x 1
∴ ? = 16 hours = 48 men need to work these many hours per day
Men = M; Days = D; Time/Hours = T; Work = W
M1D1T1W2 = M2D2T2W1
Note that - W2 is on left side and W1 is on right side
Take work done = 1
Let number of sailors who could not board = S.
So sailors who boarded = 2500-S
∴ 2500 sailors x 40 days x 1 = (2500-S) sailors x 50 days x 1
∴ S = 500 = Sailors who could not board the ship.
Total people after guests come = 75+15 = 90
75 people x 35 days x 1 = 90 people x ? days x 1
∴ ? = 29.1 days = Supplies will last for these many days
Men = M; Days = D; Time/Hours = T; Work = W
M1D1T1W2 = M2D2T2W1
Note that - W2 is on left side and W1 is on right side
To complete work in 18 days we need either 3 men or 6 boys.
∴ 1 man = 2 boys
Take work done = 1
∴ 3 men x 18 days x 1 = (4 men + 4 boys) x ? days x 1
Remember - Convert either all men to boys or all boys to men.
∴ 6 boys x 18 days x 1 = (8 boys + 4 boys) x ? days x 1
∴ ? = 9 days = they will need these many days