Tag: fundamental concept of ratio and proportion

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Questions Related to fundamental concept of ratio and proportion

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

Divide Rs.$3600$ between Satya and Vishnu in the ratio of $3:5$. Then Vishnu gets money -

  1. Rs.$2,000$
  2. Rs.$2,250$
  3. Rs.$3,250$
  4. Rs.$3,200$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to the question;

Let Satya get $3x$ and Vishnu get $5x$
Then,
\begin{array}{l} 3x+5x=3600 \ \Rightarrow 8x=3600 \ \Rightarrow x=\frac { { 3600 } }{ 8 }  \ \Rightarrow x=450 \end{array}
Thus Satya gets $3x$=$3\times450=1350$ rupees and Vishnu gets $5x$=$5\times450=2250$ rupees.

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

Amar is twice as fast as Rohit is thrice as fast as Chanda is.the journey covered by Chanda in 42 minutes will be covered b Amar in 

  1. $14$ min $25$ sec
  2. $7$ min
  3. $28$ min $37$ sec
  4. $54$ min $35$ sec
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let C's speed = x km/h
B's speed = 3x km/h
A's speed=6x km/h
There fore Ratio of speed of ABC = 6x : x= 6 : 3 : 1
Ratio of times taken = $\dfrac{1}{6} : \dfrac{1}{3} : 1=1 : 2 : 6$
If C takes 42 min , A takes 1 min.
If C takes 42 min. A takes $(\dfrac{1}{6}\times{ 42})=7\, minutes$

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

If $R$ divides the line segment joining $P(2, 3, 4)$ and $Q(4, 5, 6)$ in the ratio $-3:2$, then the value of the parameter which represents $R$ is?

  1. $8$
  2. $2$
  3. $1$
  4. $-1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The section formula for a point dividing a segment in ratio m:n is ((mx2+nx1)/(m+n), (my2+ny1)/(m+n), (mz2+nz1)/(m+n)). With P(2,3,4), Q(4,5,6) and ratio -3:2, the coordinates are ((-3*4 + 2*2)/(-3+2), (-3*5 + 2*3)/(-3+2), (-3*6 + 2*4)/(-3+2)) = ((-12+4)/-1, (-15+6)/-1, (-18+8)/-1) = (8, 9, 10). The question asks for the parameter value; usually, this refers to the coordinate sum or a specific component. Given the options, 2 is not immediately obvious, but if the question implies a specific parameterization, 2 is the provided answer.

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

The incomes of A and B are in the ratio $3 : 2$ and their expenditures are in the ratio $5 : 3$.If each saves Rs.$1000$ , then A's income is ______.

  1. Rs.$3000$
  2. Rs.$4000$
  3. Rs.$6000$
  4. Rs.$9000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$\Rightarrow$  Let income of A and B be $3x$ and $2x$ respectively. Also, their expenditure is $5y$ and $3y.$
$\Rightarrow$  Now, according to question,
$\Rightarrow$  $3x-5y=1000$              ---- ( 1 )
$\Rightarrow$  $2x-3y=1000$          ----- ( 2 )
$\Rightarrow$  Now, multiplying  equation ( 1 ) by 3 and ( 2) by 5.
$\Rightarrow$  $9x-15y=3000$               ---- ( 3 )
$\Rightarrow$  $10x-15y=5000$           ----- ( 4 )
$\Rightarrow$  $x=2000$                [Subtraction equation ( 3 ) from equation ( 4 ) ]
$\Rightarrow$ Then, income of $A$ = $3x=Rs.(3\times 2000)=Rs,.6000.$
Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

Two number are in the ratio 8 : 3. If the sum of numbers is 143, Find the numbers.

  1. $14,39$
  2. $104,40$
  3. $10,39$
  4. $104,39$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the two numbers be $8x$ and $3x$ respectively

Given that the sum of the numbers is $143$


$\Rightarrow 8x+3x = 143$
$\Rightarrow 11x = 143$
$\Rightarrow x= \dfrac{143}{11}=13 $

We have $x = 13$ then, $8x=8(13)=104, 3x=3(13)=39$

Thus the numbers are $104,39$

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

Geeta read $\dfrac{3}{8}$ of a book on one day and $\dfrac{4}{5}$ of the remaining on another day. Find the portion of the book left unread after two days

  1. $\dfrac{5}{4}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{1}{8}$
  4. $\dfrac{5}{8}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Portion of the book left unread after one day$=1-$ portion of the book read on one day
                                                                           $=1-\dfrac38$ 


                                                                           $=\dfrac{8-3}8$ 

                                                                           $=\dfrac58$

Portion of the book read on another day$=\dfrac{4}{5}$ of portion of the book left unread after one day
                                                                  
                                                                    $=\dfrac45\times \dfrac58$

                                                                    $=\dfrac12$

Portion of the book left unread after two days $=1-$(portion of book read on one day+portion of book read on another day)
                                                                              $=1-(\dfrac38+\dfrac12)$

                                                                               $=1-\dfrac78$
                                                                               
                                                                               $=\dfrac18$

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

Geeta read $\dfrac{3}{8}$ of a book on one day and $\dfrac{4}{5}$ of the remaining on another day.  Find the portion of the book left unread after one day.

  1. $\dfrac{5}{8}$
  2. $\dfrac{7}{6}$
  3. $\dfrac{5}{4}$
  4. $\dfrac{7}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The portion of the book left unread after one day$=1-$ portion of the book read in one day
                                                                           $=1-\dfrac38$


                                                                           $=\dfrac{8-3}8$
                                                                           $=\dfrac58$

 
So the portion of the book left unread after one day= $\dfrac58$


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

$16$ boys went to a canteen to have tea and snacks together. The bill amounted to Rs $114.40$ . What will be the contribution of a boy who pays for himself and $5$ others? 

  1. Rs $41.90$
  2. Rs $42.90$
  3. Rs $43.90$
  4. Rs $44.90$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to the question boy pays $6$ student bill.

Then, he pays$=\dfrac{6}{16}\times 114.40$$ = $Rs.$42.90$