Tag: mixture

Multiplying any fraction by a value greater than 1 will increase its value.

Increase: Dividing a positive number by a positive, proper fraction increases the number.

Increase: As the numerator of a positive, proper fraction increases, the value of the fraction increases. As the denominator of a positive, proper fraction decreases, the value of the fraction also increases. Both actions will work to increase the value of the fraction.

Stay the same: Multiplying or dividing the numerator and denominator of a fraction by the same number will not change the value of the fraction.

Let the new quantity be x
$\therefore \dfrac {\text {Original quantity}}{\text {New quantity}}$
$\dfrac {245}{x} = \dfrac {7}{4}$
$\therefore x = 140$
Hence, on decreasing $245$ by $4 : 7$ we get $140$ kg.

$3 : 4$ is the ratio of the new quantity to the original quantity.
Let the new number be x.
$\therefore \dfrac {x}{60} = \dfrac {3}{4}$
$\therefore x = 45$
$\therefore$ The decreased quantity is $45$

New price $= 20$
Old price $= 15$
Multiplying ratio
$\dfrac {\text {new price}}{\text {old price}} = \dfrac {20}{15} = \dfrac {4}{5}$

Let the new price of pencil box be x
$\dfrac {\text {Original price}}{\text {New price}}$
$\therefore \dfrac {70}{x} = \dfrac {14}{3}$
$\therefore x = 65$
Hence the reduced price of pencil box is Rs $65$.

Final quantity $= 63$
Original quantity $= 90$
Multiplying ratio
$\dfrac {\text {Final quantities}}{\text {Original quantity}} = \dfrac {63}{90} = \dfrac {7}{10}$

Value=$540\times \dfrac{2}{3}=360$