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Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

The difference of the squares is of two numbers is 80% of the sum of their squares The ratio of the larger number to the smaller number is

  1. 5 : 2

  2. 2 : 5

  3. 3 : 1

  4. 1 : 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the two numbers be x and y Then $\displaystyle x^{2}-y^{2}=80\%$ of $\displaystyle (x^{2}+y^{2})$
$\displaystyle \Rightarrow x^{2}-y^{2}=\frac{4}{5}(x^{2}+y^{2})\Rightarrow x^{2}-\frac{4}{5}x^{2}=\frac{4}{5}y^{2}+y^{2}$
$\displaystyle \Rightarrow \frac{1}{5}x^{2}=\frac{9}{5}y^{2}\Rightarrow \frac{x^{2}}{y^{2}}=\frac{9}{1}\Rightarrow \frac{x}{y}=\frac{3}{1}\Rightarrow x:y=3:1$

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

If a, b, c, d are positive real number such that $\frac {a}{3}=\frac {a+b}{4}=\frac {a+b+c}{5}=\frac {a+b+c+d}{6}$, then $\frac {a}{b+2c+3d}$ is

  1. $\frac {1}{2}$

  2. 1

  3. 2

  4. not determinable
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$a =3k$
$b=k$
$c= 5k-4k =k$
$d =6k-5k =k$
$\frac {a}{b+2c+3d}=\frac {3k}{k+2k+3k}=\frac {1}{2}$

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

The incomes of A, B and C are in the ratio 7 : 9 : 12 and their spendings are in the ratio 8 : 9 : 15. If A saves $\displaystyle \left ( 1/4 \right )^{th}$ of his income then?

  1. $56 : 99 : 69$
  2. $69 : 56 : 99$
  3. $99 : 56 : 69$
  4. $99 : 69 : 56$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Solution:

Let income of $A=7x$
Income of $B=9x$
Income of $C=12x$
and  Spendings of $A=8y$
Spendings of $B=9y$
Spendings of $C=15y$
Income=Savings + Expenditures
Savings of $A=\cfrac14\times 7x=\cfrac{7x}4$
or, $7x=\cfrac{7x}{4}+8y$
or, $21x=32y$
or, $x=\cfrac{32}{21}y$
Now,
Income of $A=7x=7\times \cfrac{32}{21}y=\cfrac{32}{3}y$
Income of $B=9x=9\times \cfrac{32}{21}y=\cfrac{96}{7}y$
Income of $C=7x=12\times \cfrac{32}{21}y=\cfrac{128}{7}y$
Now, 
Savings of $A=7x-8y=\cfrac{32}3y-8y=\cfrac83y$
Savings of $B=9x-9y=\cfrac{96}7y-9y=\cfrac{33}7y$
Savings of $C=12x-15y=\cfrac{128}7y-15y=\cfrac{23}7y$
So, Savings of $A,B$ and $C$ in ratio
$\cfrac83:\cfrac{33}{7}:\cfrac{23}{7}::56:99:69$
Hence, A is the correct option.

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

The least whole number which when subtracted from both the terms of the ratio  $6:7$  gives a ratio less than $16:21.$

  1. $2$
  2. $3$
  3. $4$
  4. $6$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the whole number is X.
Now, according to question,
(6-X) / (7-X) < 16/21
21 *(6-X) < 16 *(7-X)
126 - 21X < 112 - 16X
126 - 112 < -16X + 21X
14 < 5X
5X > 14
X > 2.8
So, Least such whole number would be 3.

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

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

  1. $15$
  2. $18$
  3. $20$
  4. $25$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $=3\times6cm=18cm$

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

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.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

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 $3\cfrac{1}{2}$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
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.