Tag: problems on ratios

Questions Related to problems on ratios

A sum of $Rs.350$ is to be divided between $A$ and $B$ in the ratio $3:4.$ If the amount distributed in the ratio $4:3$ the amount gained by $A$ is 

maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

  1. $Rs.10$

  2. $Rs.30$

  3. $Rs.50$

  4. $Rs.100$

Show answer
Correct Option: C
Explanation:
Let $A$ got $3x$ and $B$ got $4x$. Then,

$3x+4x=350$

$7x=350$

$x=50$

Therefore, $A$ got $150 Rs.$ and $B$ got  $200 Rs.$.

If the ratio was $4 : 3,$ $A$ got $Rs. 200$ and $B$ got $Rs. 150$.

Therefore, the amount gained by $A = Rs. 50$

Instead of dividing $Rs.\,117$ among $P,Q,R$ in the ratio $\displaystyle\frac{1}{2}\colon\displaystyle\frac{1}{3}\colon\displaystyle\frac{1}{4}$, by mistake it was divided in the ratio $2\,\colon\,3\,\colon\,4$. Who gained in the transaction? 

maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

  1. only $P$

  2. only $Q$

  3. only $R$

  4. both $Q$ and $R$

Show answer
Correct Option: D
Explanation:

Desired ratio $=\displaystyle\frac{1}{2}\colon\displaystyle\frac{1}{3}\colon\displaystyle\frac{1}{4}=\displaystyle\frac{1}{2}\times12\colon\displaystyle\frac{1}{3}\times12\colon\displaystyle\frac{1}{4}\times12$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=6\colon4\colon3$
Ratio by mistake $=2\colon3\colon4=6\colon9\colon12$
Hence, it is clear that both $Q$ and $R$ gained in the transaction.

If $2$ kg of almonds cost as much as $8$ kg of walnuts and the cost of $5$ kg of almonds and $16$ kg of walnuts is Rs. $1080$, the cost of almonds per kg is

maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

  1. Rs. $160$

  2. Rs. $150$

  3. Rs. $120$

  4. Rs. $140$

Show answer
Correct Option: C
Explanation:

Let the cost of almond per kg be Rs. $x$ and cost of walnuts per kg be Rs. $y$. Then
$2x=8y\;\;\Rightarrow\;y=\displaystyle\frac{x}{4}$
Given, $5x+16y=1080$
$\Rightarrow\;5x+\displaystyle\frac{16\times\,x}{4}=1080$
$\Rightarrow\;9x=1080\,$

$\Rightarrow\,x=120$

A man encashes a cheque of $Rs. 600$ from a bank. The bank pays him money in $10$ rupee notes and $5$ rupee notes only, totalling $72.$ The ratio of the number of $10$ rupee notes to that of $5$ rupee notes is

maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

  1. $1 : 2$

  2. $2 : 1$

  3. $2 : 3$

  4. $3 : 2$

Show answer
Correct Option: B
Explanation:

Let the number of 10 rupee notes = x. Then,
Number of 5 rupee notes = 72 - x
Given, $x \times 10 + 5 (72 - x) = 600$
$\Rightarrow 10x + 360 - 5x = 600 \Rightarrow 5x = 240 \Rightarrow x = 48$
$\therefore$ Required ratio $= \displaystyle \frac{48}{(72 - 48)} = \frac{48}{24} = \frac{2}{1} =2 : 1$

46.3=_______________

maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

  1. $\displaystyle \frac{46}{10}$

  2. $\displaystyle \frac{460}{10}$

  3. $\displaystyle 46\frac{3}{10}$

  4. $\displaystyle \frac{463}{100}$

Show answer
Correct Option: C
Explanation:

46.3 is the number we have to convert in a fraction. 

First we'll convert the given decimal in a fraction to eliminate the decimal point.
46.3=463/10
Now we divide 463 by 10.
 10×46=460 so the remainder is 3.
The resulting fraction will be, 46 whole 3/10.
So option C is the correct answer.

If Rs. $60$ is divided into two parts in the ratio $2 : 3,$ then the difference between those two parts is ______

maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

  1. Rs. $10$

  2. Rs. $12$

  3. Rs. $5$

  4. none

Show answer
Correct Option: B
Explanation:

Rs. $60$ is divided into two parts $2:3$.
Their sum is $2+3=5$.
Thus first part is $60\, \times\, \displaystyle \frac {2}{5} =$ Rs. $24$
and second part will be $60\, \times\, \displaystyle \frac {3}{5}\, =$ Rs. $36$.
Therefore, difference will be $ 36 - 24 =$ Rs. $12$.

A number $351$ is divided into two parts in the ratio $2 : 7.$ Find the product of the numbers.

maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

  1. $20,294$

  2. $21,294$

  3. $25,295$

  4. $31,294$

Show answer
Correct Option: B
Explanation:

Let the numbers be $2x$ and $7x$.
$2x + 7x = 351$
$x = 39$
Therefore, product of the numbers is $2x \times 7x$ $=$ $14x^2$
$=$ $14\, \times\, (39)^2$
$= 21,294$

The ratio of the heights of A and B is $4 : 3$ . If B is $1.2$m tall then the height of A is:

maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

  1. $0.9$ m

  2. $1.8$ m

  3. $1.6$ m

  4. none of these

Show answer
Correct Option: C
Explanation:

Height of A $\displaystyle =\frac{4}{3}\times$ height of B
                    

                    $\displaystyle =\dfrac{4}{3} \times 1.2 = 1.6$ m

The sum of the squares of three numbers which are in the ratio $2 : 3 : 4$ is $725.$ What are these numbers?

maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

  1. $10, 15, 20$

  2. $14, 21, 28$

  3. $20, 15, 30$

  4. $20, 30, 40$

Show answer
Correct Option: A
Explanation:

Let the three numbers be 2x, 3x and 4x.
Given, $(2x)^2 + (3x)^2 + (4x)^2 = 725$
$\Rightarrow 4x^2 + 9x^2 + 16 x^2 = 725 \Rightarrow 29 x^2 = 725$
$\Rightarrow x^2 = 25 \Rightarrow x = 5$
$\therefore$ The numbers are 10, 15 and 20.

The ratio of two numbers is $2:6$ and their difference is $84$. The largest number is-

maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

  1. $124$

  2. $126$

  3. $118$

  4. $226$

Show answer
Correct Option: B
Explanation:

Let the numbers be $2x$ and $6x$
We have,
$6x-2x=84$
 $4x=84$
 $x=21$
Largest number $=6x$
$=6\times 21=126$