Tag: maths

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Questions Related to maths

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

If $Rs.50$ is distributed among $150$ children giving $50p$ to each boy and $25p$ to each girl, then the number of boys is:

  1. $25$
  2. $40$
  3. $36$
  4. $50$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let the number of boys $= x$
then number of girls $= 150-x$ 
According to the problem, the total money divided between girls and boys are:
$\cfrac { 50 }{ 100 } \times  (x)+\cfrac { 25 }{ 100 } (150x)=50$
Multiply equation by $100$, we get
$50x+(150x)25 = 5000$
$\Rightarrow 50x+375025x = 5000$
$\Rightarrow 25x = 1250$
$\Rightarrow x = 50$
Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

IF the lines $ \displaystyle y=m _{1}x+c $  and $  y=m _{2}x+c _{2}  $ are parallel , then 

  1. $ \displaystyle m _{1}=m _{2} $
  2. $ \displaystyle m _{1}=m _{2} =1 $
  3. $ \displaystyle m _{1}=m _{2} =-1 $
  4. $ \displaystyle m _{1}=m _{2} =0 $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Two lines are said to be parallel if the slopes of two line will be equal
$m _1=m _2$

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

Seamus has $3$ times as many marbles as Ronit, and Taj has $7$ times as many marbles as Ronit. If Seamus has $s$ marbles then, in terms of $s$, how many marbles do Seamus, Ronit and Taj have together?

  1. $\cfrac{3}{7}s$
  2. $\cfrac{7}{3}s$
  3. $\cfrac{11}{3}s$
  4. $7s$
  5. $11s$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The problem will be easier to solve if you can choose numbers that will give you all integers as you solve. both Seamus and Taj have a multiple of the number of marbles that Ronit has, so begin by picking for Ronit, not for Seamus.
If Ronit has $2$ marbles, then Seamus has $(3)(2)=6$ marbles and Taj has $(7)(2)=14$ marbles. Together, the three have $22$ marbles.
plug $s=6$ into the answer (remember that the problem asks about Seamus's starting number, not Ronit's and look for a match of $22$:
(A) $\cfrac{3}{7}s=$ not an integer
(B) $\cfrac{7}{3}s=\cfrac{7}{3}(6)=14$. Not a match
(C) $\cfrac{11}{3}s=\cfrac{11}{3}(6)=22$. Match!!
(D) $7s=42$. Not a match
(E) $11s=$ Too large
Alternately, you can use an algebraic approach. Begin by translating the first sentence into equations:
$s=3r$
$t=7r$
The question asks for the sum of the three:
$s+r+t=$?
The answer use only $s$, so figure out how to substitute to leave only $s$ in the equation
$r=\cfrac{s}{3}$
$t=7r=7(\cfrac{s}{3})$
Substitute those into the equation
$s+r+t$
$s+\cfrac{s}{3}+7(\cfrac{s}{3})$
$\cfrac{3s}{3}+\cfrac{s}{3}+\cfrac{7s}{3}$
$\cfrac{11s}{3}$
The correct answer is (C)