Tag: dividing a quantity in a given ratio

Questions Related to dividing a quantity in a given ratio

The average age of three boys is $25$ years and their ages are in the ratio $ 3: 5 : 7$. The age of the youngest boy is

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

  1. $21$ years

  2. $18$ years

  3. $15$ years

  4. $9$ years

Show answer
Correct Option: C
Explanation:

Total age of $3$ boys $= (25 $ $\times$ $3)$ years $=75$ years. 

Ratio of their ages $ = 3 : 5 : 7$.
Age of the youngest $=$ $\displaystyle {\left (75\, \times\, \frac{3}{15} \right )}$ years $= 15$ years

An amount of money is to be divided among $P, Q$ and $R$ in the ratio $4 : 7 : 9.$ If the difference between the shares of $Q$ and $R$ is Rs. $500,$ what will be the difference between the shares of $P$ and $Q$?

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

  1. Rs. $500$

  2. Rs. $1000$

  3. Rs. $750$

  4. Rs. $850$

Show answer
Correct Option: C
Explanation:

Let the shares of $P, Q$ and $R$ be Rs. $ 4x$, Rs. $7x$ and Rs. $ 9x$ respectively. 

Then, $9x - 7x = 500$
$\Rightarrow 2x = 500$
$ \Rightarrow x = 250$
$\therefore$ required difference $= 7x - 4x = 3x = 3 \times 250 =$ Rs. $750$.

The whole number whose sum is $72$ cannot be in the ratio

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

  1. $\dfrac{5}{7}$

  2. $\dfrac{3}{5}$

  3. $\dfrac{3}{4}$

  4. $\dfrac{4}{5}$

Show answer
Correct Option: C
Explanation:

The whole number must   be divided by sum of two ratio particularly

A.$5+7=12$
$72$ can be divided by $12$

B.$ 3+5=8$
$72$ can be divided by $8$

C.$ 4+3=7$
$72$ can not be divided by $7$

D.$4+5=9$
$72$ can be divided by $9$

In a zoo, deer and lions are in the ratio of $5:2$. If there are $20$ deer then how many lions are there ?

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

  1. $4$

  2. $6$

  3. $8$

  4. $10$

Show answer
Correct Option: C
Explanation:

Let number of Deer $= 5x$
And number of lions $= 2x$
Given number of deer $= 20$
$\Rightarrow 5x = 20$
$\Rightarrow x = \dfrac{20}{5} = 4$
Thus, number of lions $= 2x = 2\cdot 4 = 8$

Four taps can individually fill a cistern of water in $1$ hour, $2$ hours, $3$ hours and $6$ hours respectively. If all the four taps are opened simultaneously, the cistern can be filled in how many minutes?

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

  1. $20$

  2. $30$

  3. $35$

  4. $40$

Show answer
Correct Option: B
Explanation:

$4$ taps individually fill a cistern of water in $1$ hour, $2$ hours, $3$ hours and $6$ hours.
Part of the cistern filled in one hour
$= \left (1 + \dfrac {1}{2} + \dfrac {1}{3} + \dfrac {1}{6}\right ) = 2$
$\Rightarrow$ Twice the capacity is full in $60$ min.
Therefore, cistern is full in $30$ min.

If a carton containing a dozen mirrors is dropped, which of the following cannot be the ratio

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

  1. $2:1$

  2. $3:1$

  3. $3:2$

  4. $7:5$

Show answer
Correct Option: C
Explanation:

For dividing $12$ into two whole numbers, the sum of the ratios must be a factor of $12$. So they cannot be in the ratio $3:2$

If Rs 782 be divided into three parts proportional to $\dfrac{1}{2} : \dfrac{2}{3} : \dfrac{3}{4} $ then the first part is

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

  1. $Rs.\ 182$

  2. $Rs.\ 190$

  3. $Rs.\ 196$

  4. $Rs.\ 204$

Show answer
Correct Option: D
Explanation:

Given ratio = $\dfrac{1}{2} : \dfrac{2}{3} : \dfrac{3}{4} $     ...............   Multiplying by $12$ 


                    = $6:8:9$


$\therefore$ 1st part = Rs. $\left ( 782 \times \dfrac{6}{23} \right )$ = Rs. $204$

Of the $126$ students who applied for a full scholarship at Oxbow College, $9$ received one. What is the ratio of students who received a scholarship to those who didnt?

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

  1. $1$ to $10$

  2. $1$ to $11$

  3. $1$ to $12$

  4. $1$ to $13$

  5. $1$ to $14$

Show answer
Correct Option: D
Explanation:

Given,
No of students who applied for scholarship $=126$
No of students who got scholarship $=9$
No of students who didn't get scholarship $=126-9=117$
Ratio of students who received a scholarship to those who didn't is $9:117=1:13$.

If Rs. $2,600$ is divided among three persons $A, B$ and $C$ in the ratio $\dfrac {1}{2} : \dfrac {1}{3} : \dfrac {1}{4}$, how much does $A$ get?

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

  1. Rs. $ 600$

  2. Rs. $ 800$

  3. Rs. $ 1.000$

  4. Rs. $ 1,200$

Show answer
Correct Option: D
Explanation:

Among three persons Rs. $2600$ is divided in the ratio as $\dfrac {1}{2}, \dfrac {1}{3}, \dfrac {1}{4}$.
LCM of $\dfrac {1}{2} : \dfrac {1}{3} : \dfrac {1}{4} $ is $ 6 : 4 : 3$.
Therefore, $A$'s share $= \dfrac {6}{13} \times  2,600 =$ Rs. $1,200$.

Three numbers are in the ratio $3 : 2 : 5$ and the sum of their squares is $1862$. What are the three numbers?

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

  1. $18, 12, 30$

  2. $24, 16, 40$

  3. $15, 10, 25$

  4. $21, 14, 35$

Show answer
Correct Option: D
Explanation:

Let the three numbers b $3x, 2x, 5x$

Sum of their squares is $1862$.
Therefore, $(3x)^{2} + (2x)^{2} + (5x)^{2} = 1862$
$\Rightarrow 38x^{2} = 1862$
$\Rightarrow  x^{2} = 1862 \div 38 = 49$
$\Rightarrow x = 7$ 
The numbers are $21, 14, 35$.