Tag: division problem

Questions Related to division problem

Kamal started a business investing Rs.$9000$. After five months, Sameer joined with a capital of $Rs.8000$. If at the end of the year, they earn a profit of $Rs.6970$, then what will be the share of Sameer in the profit?

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

  1. $Rs.2370$

  2. $Rs.2380$

  3. $Rs.2390$

  4. $Rs.2280$

Show answer
Correct Option: B
Explanation:

Now as per question, Kamal invested for $12$ months and Sameer invested for $7$ months.
So, Kamal:Sameer=$\begin{pmatrix}9000\times12\end{pmatrix}:\begin{pmatrix}8000\times7\end{pmatrix}$
$=108.56=27:14$
Sameer ratio in profit will be $=6970\times \dfrac{14}{41}=Rs.2380$

In a mixture $60$ litres, the ratio of milk and water $2:1$. If this ratio is to be $1:2$, then the quantity of water to be further added is

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

  1. $30$

  2. $40$

  3. $50$

  4. $60$

Show answer
Correct Option: D
Explanation:

Quantity of milk $=60\times \dfrac{2}{3}=40$ litres
Quantity of water $=60-40=20$ litres
As per question we need to add water to get quantity $2:1$
$\Longrightarrow \dfrac{40}{20+x}=\dfrac{1}{2}$
$\Rightarrow\;20+x=80$
$\Rightarrow\;x=60$ litres

A basket has 30 items, find the number of items that two persons A and B gets if the the items are divided in the ratio of 2:3.

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

  1. 14 and 16

  2. 12 and 18

  3. 9 and 21

  4. none of these

Show answer
Correct Option: B
Explanation:

Since the ratio is $2:3$,

Let A receives $2x$ items then B will receive $3x$ items
But the total items in the basket is $30$, so
$2x+3x=30\Rightarrow 5x=30\Rightarrow x=6$
So person A will get 12 and person B will get 18 items 

A box contains coins of 50 paise, 1 rupee and 2 rupees. For 240 coins in the box, the ratio of 50 paise to 1 rupee to 2 rupees is 8 : 17 : 15. How many 1 rupee coins are there in the box ?

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

  1. 48

  2. 90

  3. 102

  4. 108

Show answer
Correct Option: C
Explanation:

$ Let\quad number\quad of\quad 50\quad paise\quad coin=a\ \quad \quad \quad number\quad of\quad 1\quad Rs\quad coin=b\ \quad \quad \quad number\quad of\quad 2\quad Rs\quad coin=c\ \therefore \quad Given\quad a:b:c=8:17:15\ \therefore \quad b's\quad part\quad is\quad \frac { 17 }{ 8+17+15 } =\frac { 17 }{ 40 } \ \therefore \quad Actual\quad number\quad of\quad b\quad is\quad \frac { 17 }{ 40 } \times 240=102\ \therefore \quad Number\quad of\quad 1\ Rs\quad coin\quad is\quad 102.\quad \quad (Ans) $

If the ratio of men to women in an office is $7$ to $5$. Which of the following could not be the number of employees in the office ?

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

  1. 24

  2. 30

  3. 36

  4. 48

Show answer
Correct Option: B
Explanation:

According to the problem, there are $7$ men for every $5$ women in the office.
Let the number of men and women be $7x$ and $5x$ respectively.
This means that the total number of employees will always be a multiple of $(7x+5x)=12x$.
From the given options, $30$ is not a multiple of $12$.
So, the required answer is $30$.

Two numbers are in the ratio $3 : 5$. If the sum of numbers is $144$, then the small number is 

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

  1. $54$

  2. $72$

  3. $90$

  4. $48$

Show answer
Correct Option: A
Explanation:

$Let\quad the\quad numbers\quad be\quad 3x\quad and\quad 5x.\$ 


$3x+5x=144\ $

$8x=144$

$x=18$

$Smaller\quad no.=3x=3×18=54$

In the word MATHEMATICS , the ratio of number of consonants to the number of vowels is _____ .

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

  1. $4 : 7$

  2. $7 : 4$

  3. $5 : 6$

  4. $6 : 5$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  Consonants in the given word are = $M,T,H,M,T,C,S$

$\therefore$  Total number of consonants = $7$
$\Rightarrow$  Vowels in the given words are = $A,E,A,I$
$\therefore$  Total number of vowels = $4$.

$\therefore$  $\dfrac{Number\,of\,consonants}{Number\,of\,viwels}=\dfrac{7}{4}$

$\therefore$   Required ratio is $7:4$

A sum of Rs. 9,000 is to be distributed among A, B and C in the ratio of 4 : 5 : 6. What will be the difference between As and Cs shares?

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

  1. Rs. 600

  2. Rs. 1,000

  3. Rs. 900

  4. Rs. 1,200

Show answer
Correct Option: D
Explanation:

Given that,
Total money = Rs. 9000 
A: B: C = 4 :5:6 
As share= $\cfrac{4}{(4 + 5 + 6)} \times 9000 = 2400$
Bs share = $\cfrac{5}{(4 + 5 + 6)} \times 9000 = 3000$
Cs share = $\cfrac{6}{(4 + 5 + 6)}\times 9000=3600$

Total money = Rs. 9000 
Hence, difference between As share and Cs share
= 3600 - 2400 = 1200

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

  1. $5 : 6$

  2. $11 : 8$

  3. $25 : 18$

  4. $27 : 16$

Show answer
Correct Option: C
Explanation:

It is given that,
$\dfrac {l _{1}}{l _{2}} = \dfrac {5}{3}$ and $\dfrac {s _{1}}{s _{2}} = \dfrac {6}{5}\Rightarrow \dfrac {t _{1}}{t _{2}} = \dfrac {\dfrac {l _{1}}{s _{1}}}{\dfrac {l _{2}}{s _{2}}} = \dfrac {l _{1}}{l _{2}}\times \dfrac {s _{2}}{s _{1}} = \dfrac {5}{3}\times \dfrac {5}{6} = \dfrac {25}{18}$
Hence, $t _{1} : t _{2} = 25 : 18$.