Tag: maths

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Questions Related to maths

Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

Find the value of $\displaystyle\left(\frac{P+Q}{R}\right)\times S$.
(i) $100$ lakhs $=$ _________[Q] millions
(ii) ____[R] crores $=100$ millions
(iii) $100$ thousands $=$ ___[P] lakhs
(iv) $10$ crores $=$ _______[S] millions.

  1. $10$
  2. $100$
  3. $110$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$1$ Million $=$ $10$ lakh
$100$lakh $=$ Q million
Q $=$ ($100$/$10$) $=$$10$
R crore $=$ $100$ Million
R $=$ ($100$X$1000000$) / ($10000000$)
R $=$ $10$
$100$ X $1000$ $=$ $1$lakh $=$ P lakhs
P $=$ $1$
$10$X$10000000$ $=$ S Million
S $=$ $100000000$/$1000000$
S $=$  $100$
So, P $=$ $1$,   Q $=$ $10$,  R $=$ $10$,  S $=$ $100$
P $+$ Q  $=$ $11$
$\dfrac{(P+Q)}{R}=$ $11/10$
$\left(\dfrac{(P+Q)}{R}\right)\times S=\dfrac{11}{10}\times 100$ $=$ $110$
Hence, option C is correct.
Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

If $\dfrac{1}{x} + y = 3$ and $x + \dfrac{1}{y} = 2$ then $x:y$ is 

  1. $3:2$
  2. $2:3$
  3. $1:2$
  4. $2:1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The question states '...then x: is' 
It should state '..then x:y is'

Given
$\dfrac { 1 }{ x } +y=3$ --- Eqn (1)
$x+\dfrac { 1 }{ y } =2$ ---Eqn (2)

Multiplying Eqn (1) by x and Eqn (2) by y, we get:

$x\left( \dfrac { 1 }{ x } +y \right) =3x\quad \Rightarrow 1+yx=3x$ --- Eqn (3)
$y\left( x+\dfrac { 1 }{ y }  \right) =2y\quad \Rightarrow xy+1=2y$ --- Eqn (4)

Subtracting Eqn (4) and Eqn (5), we get:

$1+yx-1-yx=3x-2y$
$\Rightarrow 0=3x-2y$
$\Rightarrow 3x=2y$
$\Rightarrow \dfrac { x }{ y } =\dfrac { 2 }{ 3 } $
$\therefore x:y=2:3$

Hence the answer is B
Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

If ${x+y}{ax+by}=\dfrac{y+z}{ay+bz}=\dfrac{z+x}{az+bx}$, then "each of these ratio is equal to $\dfrac{2}{a+b}$, unless $x+y+z=0$." this statement is ____

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the property of ratios, if a/b = c/d = e/f, then each ratio is equal to (a+c+e)/(b+d+f). Adding the numerators gives 2(x+y+z) and adding the denominators gives (a+b)(x+y+z). Canceling (x+y+z) yields 2/(a+b).