Tag: maths

Questions Related to maths

What is the average of all numbers between $11$ and $80$ which are divisible by $6$?

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

  1. $46$

  2. $47$

  3. $44$

  4. $45$

Show answer
Correct Option: D
Explanation:

Required average $= \dfrac {12 + 18 + 24 + .... + 78}{12} = 45$.

What is the remainder when $6729$ is divided by $35$?

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

  1. $11$

  2. $7$

  3. $9$

  4. $13$

Show answer
Correct Option: C
Explanation:

$6729 = 6720 + 9 = 35\times 192 + 9$
Hence the remainder is $9$.

The estimated product of $15289$ and $587$ is

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

  1. $8000000$

  2. $8500000$

  3. $9000000$

  4. $9500000$

Show answer
Correct Option: C
Explanation:

$15289$ is estimated as $15300$ and $587$ is estimated as $600$.

So, the given product is estimated as $153000\times 600=918,0000$.
So the correct estimate is $900,0000$.

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.

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

  1. $10$

  2. $100$

  3. $110$

  4. $1$

Show answer
Correct Option: C
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.

Convert the following into percentage.
$\dfrac{2}{3}$.

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $66\%$

  2. $65\%$

  3. $33\%$

  4. $66.67\%$

Show answer
Correct Option: D
Explanation:
$\dfrac{2}{3}$ into percentage
$=\dfrac{2}{3}\times 100\%= \dfrac{200}{3}\% = 66.67\%$

Convert the following into percentage.
$\dfrac{5}{8}$.

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $62.5 \%$

  2. $65.5\%$

  3. $66.6\%$

  4. $64\%$

Show answer
Correct Option: A
Explanation:
$\dfrac{5}{8}$
$=\dfrac{5}{8}\times 100\%=\dfrac{500}{8}\%=62.5\%$

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

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $3:2$

  2. $2:3$

  3. $1:2$

  4. $2:1$

Show answer
Correct Option: B
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

Find the ratio of: $36$ to $64$

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $9:11$

  2. $9:12$

  3. $9:16$

  4. $9:17$

Show answer
Correct Option: C
Explanation:

$\dfrac{36}{64}=\dfrac{36\div 4}{64\div 4} =\dfrac{9}{16}$

The ratio of $40\ min$ to $2.5$ hours is

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. $4:17$

  2. $4:18$

  3. $4:13$

  4. $4:15$

Show answer
Correct Option: D
Explanation:
$\dfrac {40\ min}{2.5\ hr}$
$=\dfrac {10\ min}{2hr +30\ min}=\dfrac {40}{2\times 60+30}$
$=\dfrac {40}{150}\ \Rightarrow \boxed {4:15}$
Option $D$ is correct

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 ____

maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

  1. True

  2. False

Show answer
Correct Option: A