Tag: types of ratios

Questions Related to types of ratios

The difference between the numerator and the denominator of a fraction is $5$ If $5$ is added to the denominator the fraction is decreased by $\displaystyle 1\frac{1}{4}$ then the value of the fraction will be equal to:

maths mixture types of ratios ratios in proportion mathematical logic

  1. $\displaystyle \frac{1}{6}$

  2. $\displaystyle 2\frac{1}{4}$

  3. $\displaystyle 3\frac{1}{4}$

  4. $6$

Show answer
Correct Option: B
Explanation:

Let the numerator be $x+5$ and denominator be $x$


Given condition is :$\dfrac {x+5}{x}-\dfrac {x+5}{x+5}=\dfrac {5}{4}$

$\Rightarrow \dfrac {x+5}{x}=\dfrac {9}{4}=2\dfrac {1}{4}=$fraction value 

$\therefore $fraction value$ =2\dfrac {1}{4}$

Seats for Mathematics, Physics and Biology in a school are in the ratio $5 : 7 : 8$.  There is a proposal to increase these seats by $40\%$, $50\%$ and $75\%$ respectively. What will be the ratio of increased seats?

maths mixture types of ratios ratios in proportion mathematical logic

  1. $2 : 3 : 4$

  2. $6 : 7 : 8$

  3. $6 : 8 : 9$

  4. None of these

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Correct Option: A
Explanation:

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are ($140\%$ of $5x$), ($150\%$ of  $7x$) and ($175\%$ of $8x$).
 $\rightarrow \left ( \dfrac{140}{100} x\times  5x\right ),\left ( \dfrac{150}{100} x\times 7x\right ), and \left ( \dfrac{175}{100} \times  8x\right )$
$\rightarrow 7x, \dfrac{21x}{2}$ and $14x$
$\therefore $ The required ratio$ = 7x:$ $\dfrac{21x}{2}$$: 14x$
$\rightarrow$ $14x : 21x : 28x$
$\rightarrow$ $2 : 3 : 4$

The present population of a city is 8000 if it increases by $10\%$ during the first year and by $20\%$ during the second year , then population after two years will be 

maths mixture types of ratios ratios in proportion mathematical logic

  1. 12400

  2. 14400

  3. 10560

  4. None of these

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Correct Option: C
Explanation:

Population after two years,
$=8000\times \dfrac{110}{100}\times \dfrac{120}{100}=10560$

The population of a bacteria culture doubles in number every 12 minutes. The ratio of the number of bacteria at the end of 1 hour to the number of bacteria at the beginning of that hour is

maths mixture types of ratios ratios in proportion mathematical logic

  1. $8 : 1$

  2. $16 : 1$

  3. $32 : 1$

  4. $60 : 1$

Show answer
Correct Option: C
Explanation:

If a number is multiplies repeatedly by 2 for n times then the last result will be $ { 2 }^{ n }\times number $.
Let  the number of bacteria is $a$. The number of bacteria doubles every $12$   minutes, which means that it doubles $5$ times in an hour.
Therefore,
$(2)(2)(2)(2)(2)a =a\times2^5$
                            $ = 32 a$  at the end of the hour.
Thus, the ratio of the number of bacteria at the end of 1 hour to the number of bacteria at the beginning of that hour is $\cfrac{32a}{a} = 32:1$.

A shopkeeper brought two $TV$ sets at $Rs. 10,000$ each. He sold one at a profit of $10\%$ and the another at a loss of $10\%$. Find his total profit or loss.

maths mixture types of ratios ratios in proportion mathematical logic

  1. $20 \%$

  2. $0 \%$

  3. $10 \%$

  4. $5 \%$

Show answer
Correct Option: B
Explanation:

Given that cost of two TV sets is $Rs.10,000$ each


One was sold at a profit of $10\%$ and

the other at a loss of $10\%$

Therefore, the total cost is $20,000+10000\times0.1-10000\times0.1=20,000$

Hence, the total profit or loss percentage is $0$

A year ago, the cost of Maruti and Figo are in the ratio of $3 : 4$. The ratio of present and past year costs of Maruti and Figo are $3 : 2$. Find the ratio of present costs

maths mixture types of ratios ratios in proportion mathematical logic

  1. $\dfrac98$

  2. $\dfrac38$

  3. $\dfrac58$

  4. $\dfrac97$

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Correct Option: A

One year ago, the ratio between Ram's and Shyam's salaries was $3 : 5$. The ratio of their individual salaries of last year and present year are $2 : 3$ and $4 : 5$ respectively. If their total salaries for the present year is $Rs. 8600$, find the present salary of Ram ?

maths mixture types of ratios ratios in proportion mathematical logic

  1. $3200$

  2. $3600$

  3. $4000$

  4. $4400$

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Correct Option: B

The ratio of the number of student studying in schools A, B and C is $6:8:7$ respectively if the number of student studying in each of the schools is increased by $20\%,15\%$ and $20\%$ respectively then what will be the new ratio of the number of student in school A, B and C ?

maths mixture types of ratios ratios in proportion mathematical logic

  1. $18:23:21$

  2. $16:28:30$

  3. $20:12:36$

  4. $22:21:12$

Show answer
Correct Option: A
Explanation:
The ratio of the number of students studying in school A, B, C.
$= 6 : 8 : 7$

Suppose number of student's in school
$A=6x$
$B=8x$
$C= 7x$

It will be Increased by
$A= 6x + 6x \times 20$ %

$= 6x+\dfrac {6x\times 20}{100}$

$= 6x+\dfrac {6x}{5}$

$= \dfrac {30x+6x}{5}$

$=\dfrac {36 x}{5}$

$B = 8x +\dfrac {8x \times 15}{100}$

$ =8x +\dfrac {6x}{5}$

$ = \dfrac {46x}{5}$

$C= 7x+\dfrac {7x\times 20}{100}$

$=\dfrac {35x +7x}{5}$

$=\dfrac {42 x}{5}$

New Ratio $= \dfrac {36 x}{5}:\dfrac {46 x}{5}: \dfrac {42 x}{5}$

$ =36:  46 : 42$

$ = 18  : 23  : 21$

Suppose $x$ and $y$ are inversely proportional and positive. If $x$ increases $p\%$ then $y$ decreases by  

maths mixture types of ratios ratios in proportion mathematical logic

  1. $p\%$

  2. $\dfrac{p}{1+p}\%$

  3. $\dfrac{100}{p}\%$

  4. $\dfrac{100p}{100+p}\%$

Show answer
Correct Option: D
Explanation:

It is given that $x$ and $y$ are inversely proportional


$x\propto \cfrac{1}{y}$


$\Rightarrow$ $xy=$ constant

${x} _{1}{y} _{1}={x} _{2}{y} _{2}...(1)$

$x$ has $p$ percent increase

${x} _{2}={x} _{1}\left(1+\cfrac{p}{100}\right)$

${x} _{1}{y} _{1}={x} _{2}{y} _{2}$

${x} _{1}{y} _{1}={x} _{1}\left(1+\cfrac{p}{100}\right){y} _{2}$

${y} _{2}=\cfrac{100{y} _{1}}{100+p}$

${y} _{2}=\left(\cfrac{100+p}{100+p}\right){y} _{1}-\cfrac{p{y} _{1}}{100+p}$

${y} _{2}-{y} _{1}=\cfrac{p{y} _{1}}{100+p}$

$\cfrac{{y} _{2}-{y} _{1}}{{y} _{1}}=-\cfrac{p}{100+p}$

$\Rightarrow$ $\cfrac{{y} _{1}-{y} _{2}}{{y} _{1}}=\cfrac{p}{100+p}$

percentage decrease $=\cfrac{{y} _{1}-{y} _{2}}{{y} _{1}}\times 100=\cfrac{100p}{100+p}$%

A jar contained a mixture of two liquids A and B in the ratio 7 : 2. When 18 litres of mixture was taken out and 18 litres of liquid B was poured into the jar. This ratio became 2 : 3. The quantity of liquid A contained in the jar initially was: 

maths mixture types of ratios ratios in proportion mathematical logic

  1. $\frac { 450 } { 17 }$ litres

  2. $\frac { 490 } { 19 }$ litres

  3. $\frac { 490 } { 17 }$ litres

  4. $\frac { 450 } { 19 }$ litres

Show answer
Correct Option: A