Tag: types of ratios

Questions Related to types of ratios

If $8 : 9$ is equal to $456: x$, then the value of $x$ is

maths mixture types of ratios ratios in proportion mathematical logic

  1. $350$

  2. $450$

  3. $600$

  4. $513$

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Correct Option: D
Explanation:

$\cfrac {456}{x} = \dfrac {8}{9}$

On cross multiplying, we get
$x = \cfrac {9 \times 456}{8}$
$\therefore x = 513$

In what ratio we must increase Rs. $750$ to obtain Rs. $1000$?

maths mixture types of ratios ratios in proportion mathematical logic

  1. $1 : 2$

  2. $5 : 6$

  3. $4 : 3$

  4. $7 : 8$

Show answer
Correct Option: C
Explanation:

Original quantity $= 750$
Final quantity $= 1000$

Multiplying ratio:
$\dfrac {\text {final quantity}}{\text {original quantity}} = \dfrac {1000}{750} = \dfrac {4}{3}$

Increasing Rs $40$ in the ratio $5 : 4$ we get?

maths mixture types of ratios ratios in proportion mathematical logic

  1. $10$

  2. $60$

  3. $50$

  4. $80$

Show answer
Correct Option: C
Explanation:

Increasing Rs $40$ in the ratio $5.4$ implies that the ratio of the new quantity to the old quantity is $5 : 4$.
$\therefore$ Let the increased quantity be x
$\therefore \dfrac {\text {New amount}}{\text {original amount}} = \dfrac {x}{40} = \dfrac {5}{4}$
$\therefore x = 50$
that is the increased quantity is $50$

Gautam's monthly salary is Rs $20000$. His salary is increased by $4 : 5$ to his new salary?

maths mixture types of ratios ratios in proportion mathematical logic

  1. $25000$

  2. $26000$

  3. $24000$

  4. $22000$

Show answer
Correct Option: A
Explanation:

Let the new salary be $x$

$\Rightarrow$ $\dfrac {\text {original salary}}{\text {new salary}}$

$\dfrac {20000}{x} = \dfrac {4}{5}$

$\therefore x = 25000$
Hence Gautam's new salary is Rs $25000$

Well-Grown potting soil is made from only peat moss and compost in a ratio of $3$ pounds of peat moss to $5$ pounds of compost. If a bag of Well-Grown potting soil contains $12$ pounds of potting soil, find how many pounds of peat moss it contains.

maths mixture types of ratios ratios in proportion mathematical logic

  1. $4.18$

  2. $4.22$

  3. $4.35$

  4. $4.50$

Show answer
Correct Option: D
Explanation:

$3$ pounds of peat moss is to $5$ pounds of compost is the composition in $8$ pounds potting soil.

Since we have $12$ pounds of potting soil, corresponding amount of peat moss becomes $\cfrac{3 \times 12}{8} = 4.5 $ pounds

Two numbers are in the ratio of $1:2$. If $7$ be added to both, their ratio changes to $3:5$. The greater number is.

maths mixture types of ratios ratios in proportion mathematical logic

  1. $20$

  2. $24$

  3. $28$

  4. $32$

Show answer
Correct Option: C
Explanation:

Let the numbers are $x$ and $y$ whose ratio is $1 : 2$

$\dfrac{x}{y}=\dfrac{1}{2}$
$\Rightarrow 2x=y$.......................................(1)
Given that when 7 added to both numbers, ratio changes to $3 : 5$
$\dfrac{x+7}{y+7}=\dfrac{3}{5}$
$\Rightarrow 5(x+7)=3(y+7)$
$\Rightarrow 5x+35=3y+21$
$\Rightarrow 5x-3y=21-35$
$\Rightarrow 5x-3y=-14$.................(2)
Put the value of $y=2x$ as per (1) we get
$5x-3(2x)=-14$
$5x-6x=-14$
$x=14$
Put the value of $x=14$ in (1) we get
$2\times 14=y$
$\Rightarrow y=28$
Then numbers are$ 14 ,28$
Then greater number is $28$.

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire rental of the car, then the share of each of the remaining persons increased by.

maths mixture types of ratios ratios in proportion mathematical logic

  1. $\dfrac{1}{9}$

  2. $\dfrac{1}{8}$

  3. $\dfrac{1}{7}$

  4. $\dfrac{7}{8}$

Show answer
Correct Option: C
Explanation:
Original share of 1 person $=\dfrac{1}{8}$
New share of 1 person $=\dfrac{1}{7}$

Then, share increased $=\dfrac{1}{7}-\dfrac{1}{8}=\dfrac{1}{56}$

So, required dfraction $=\dfrac{\dfrac{1}{56}}{\dfrac{1}{8}}=\dfrac{1}{56}\times \dfrac{8}{1}=\dfrac{1}{7}$

Negation of ''A is in Class $X^{th}$ or B is in $XII^{th}$'' is

business maths mixture types of ratios ratios in proportion mathematical logic

  1. A is not in class $X^{th}$ but B is in $XII^{th}$.

  2. A is not in class $X^{th}$ but B is not in $XII^{th}$.

  3. Either A is not in class $X^{th}$ or B is not in $XII^{th}$.

  4. none of these

Show answer
Correct Option: B
Explanation:

$\sim (p \lor q)=\sim p \land \sim q$
negaion of "A is in $X^{th}$ and B is in $XII^{th}$" is 
"A is not in $X^{th}$ and B is not in $XII^{th}$

$A, B$ and $C$ enter into partnership by making investments in the ratio $3:5:7$. After a year, $C $ invests another Rs. $337600$ while $A$ withdraws Rs. $45600$. The ratio of investments then changes to $24:59:167$. How much did $A$ invest initially?

maths mixture types of ratios ratios in proportion mathematical logic

  1. Rs. $45600$

  2. Rs. $96000$

  3. Rs. $141600$

  4. None of these

Show answer
Correct Option: C
Explanation:

Let initial investments by $A, B$ and $C$ are $3x, 5x, 7x$

After a year:
$A$'s investment $=3x-45600$
$C$'s investment $=7x +337600$
$(3x-45600):5x : (7x+337600) = 24 : 59 : 167$
Solving this we will get $x=47200$
So, A's initial investment was $=3x = 3\times47200 = 141600$

Choose the correct answer from the alternatives given.
The ratio of length of two trains is 5 : 3 and the ratio of their speed is 6: 5. The ratio of time taken by them to cross a pole is

maths mixture types of ratios ratios in proportion mathematical logic

  1. $5 :6$

  2. $11:8$

  3. $25: 18$

  4. $27: 16$

Show answer
Correct Option: C
Explanation:

It is given that,
$\displaystyle \dfrac{l _1}{l _2} \, = \, \dfrac{5}{3} \, and \, \dfrac{s _1}{s _2} \, = \, \dfrac{6}{5} \, \Rightarrow \, \dfrac{t _1}{t _2} \, = \, \frac{s _1}{l _2} \, = \, \dfrac{l _1}{l _2} \, \times \, \dfrac{s _2}{s _1} \, = \, \dfrac{5}{3} \, \times \, \dfrac{5}{6} \, = \, \dfrac{25}{18}$
Hence, $t _1 : t _2$ = $25 : 18$