Tag: mathematical logic

Questions Related to mathematical logic

The length of the ribbon was originally $30cm$. It was reduced in the ratio $5:3$. What is its length now?

maths mixture types of ratios ratios in proportion mathematical logic

  1. $15$

  2. $18$

  3. $20$

  4. $25$

Show answer
Correct Option: B
Explanation:

Length of ribbon originally $=30cm$
Let the original length be $5x$ and reduced length be $3x$.
But $5x=30cm$
$\Longrightarrow x=\dfrac{30}{5}cm=6cm$
Therefore, reduced length $=3\times6cm=18cm$

State whether true or false:
The following operation will increase the value of the original fraction:
Multiply a positive proper fraction by $\cfrac{3}{8}$.

maths mixture types of ratios ratios in proportion mathematical logic

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

Decrease: Multiplying a  proper fraction by a value less than 1 (0 < x < 1) decreases the number.

So here $3/8 = 0.375 < 1$ So, the value of original fraction decreases.

State whether true or false:
Multiplying the numerator of a positive proper fraction by $\cfrac{3}{2}$ will cause the original value to increase.
maths mixture types of ratios ratios in proportion mathematical logic

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

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

Here, $3/2 = 1.5 > 1$. So, the given statement is True.

State whether true or false:
The following operation will increase the value of the original fraction.
Divide a positive, proper fraction by $\cfrac{3}{13}$

maths mixture types of ratios ratios in proportion mathematical logic

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

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

State whether true or false
The given operation will increase the value of the original fraction.
Adding 1 to the numerator of a positive proper fraction and subtracting 1 from its denominator.

maths mixture types of ratios ratios in proportion mathematical logic

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

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.

State whether true or false:
The following operation will increase the value of the original fraction.
Multiply both the numerator and denominator of a positive proper fraction by $3\cfrac{1}{2}$.

maths mixture types of ratios ratios in proportion mathematical logic

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

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.

Decrease $245$ kg by $7 : 4$

maths mixture types of ratios ratios in proportion mathematical logic

  1. $140$

  2. $190$

  3. $150$

  4. $130$

Show answer
Correct Option: A
Explanation:

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.

After decreasing $60$ in the ratio $3 : 4$ we get?

maths mixture types of ratios ratios in proportion mathematical logic

  1. $45$

  2. $50$

  3. $40$

  4. $60$

Show answer
Correct Option: A
Explanation:

$3 : 4$ 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 $45$

If the price of a pen increases from Rs $15$ to Rs $20$, then the price has increased in the ratio of?

maths mixture types of ratios ratios in proportion mathematical logic

  1. $4 : 3$

  2. $1 : 2$

  3. $3 : 4$

  4. $9 ; 8$

Show answer
Correct Option: A
Explanation:

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

The price of pencil box is Rs $70$. If the price of pencil box is reduced by $14 : 13$ what will be the reduced price of pencil now?

maths mixture types of ratios ratios in proportion mathematical logic

  1. $60$

  2. $65$

  3. $75$

  4. $80$

Show answer
Correct Option: B
Explanation:

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 $65$.