Tag: maths

Questions Related to maths

36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?

introduction to ratio and percentages comparing quantities maths

  1. 12

  2. 18

  3. 22

  4. 24

  5. None of these

Show answer
Correct Option: D
Explanation:

Let the required number of days be x.
Less men, More days (Indirect Proportion)
$\therefore 27 : 36 :: 18 : x \Leftrightarrow 27 \times x = 36 \times 18$
$\Rightarrow x = \dfrac{36 \times 18}{27}$
$\Rightarrow x = 24$

If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

introduction to ratio and percentages comparing quantities maths

  1. 1

  2. $\dfrac{7}{2}$

  3. 7

  4. 49

Show answer
Correct Option: C
Explanation:

Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
$\left.\begin{matrix}Spiders & 1 : 7 \ Webs  &  7 : 1 \end{matrix}\right} :: 7 : x$
$\therefore 1 \times 7 \times x = 7 \times 1 \times 7$
$\Rightarrow x = 7$

Ravi and Kumar are working on as assignment. Ravi takes $6$ hours to type $32$ pages on a computer, while Kumar takes $5$ hours to type $40$ pages. How much time will they take, working together on two difference computers to type an assignment of $110$ pages?

introduction to ratio and percentages comparing quantities maths

  1. $7$ hours $30$ minutes

  2. $8$ hours

  3. $8$ hours $15$ minutes

  4. $8$ hours $25$ minutes

Show answer
Correct Option: C
Explanation:

Number of pages typed Rave in $1$ hour $=\cfrac{32}{6}=\cfrac{16}{3}$
Number of pages typed by Kumar in $1$ hour $=\cfrac{40}{5}=8$.
Number of pages typed by both in $1$ hour $=\left( \cfrac { 16 }{ 3 } +8 \right) =\cfrac { 40 }{ 3 } $.
$\therefore$ Time taken by both to type $110$ pages $=\left( 110\times \cfrac { 3 }{ 40 }  \right) $ hours
$=8\cfrac{1}{4}$ hours (or) $8$ hours $15$ minutes.

Sakshi can do a piece of work in $20$ days. Tanya is $25$% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:

introduction to ratio and percentages comparing quantities maths

  1. $15$

  2. $16$

  3. $18$

  4. $25$

Show answer
Correct Option: B
Explanation:

Ratio of times taken by Sakshi and Tany $=125:100=5:4$.
Suppose Tanya takes $x$ days to do the work.
$5:4::20:x$ $\Rightarrow \left( \cfrac { 5\times 20 }{ 5 }  \right) $
$\Rightarrow$ $x=16$ days.
Hence, Tanya takes $16$ days to complete the work.

There are four numbers whose product is $9261000$ and each of these four numbers is formed by $3$ distinct prime numbers. The average of all the four numbers is:

introduction to ratio and percentages comparing quantities maths

  1. $61.75$

  2. $67.25$

  3. $82.33$

  4. $Data\ insufficient$

Show answer
Correct Option: A

A shopkeeper offers a discount of 25% on a T.V and sells it for Rs.8400. What is the cost price of the T.V?

introduction to ratio and percentages comparing quantities maths

  1. Rs.8570

  2. Rs.11200

  3. Rs.9040

  4. Rs.8960

Show answer
Correct Option: B
Explanation:

Let the cost price of the T.V.$ = x$


After give $25\%$ discount 


$x - \dfrac{25}{100} \times x =$ selling price 
                        $= 8400$

$\dfrac{75}{100} \times x = 8400$

$\dfrac{3}{4} x = 8,400$

$x = \dfrac{8,400 \times 4}{3}$

$x = 11,200$

The temperature of a metal coin is increased ny $100^0$C and its diameter by 0.15%. Its area increases by nearly

introduction to ratio and percentages comparing quantities maths

  1. 0.15%

  2. 0.60%

  3. 0.30%

  4. 0.0225%

Show answer
Correct Option: C
Explanation:

$A = \pi r^2$
$\displaystyle \frac{\Delta A}{A} = 2 \frac{\Delta A}{r}$
$\displaystyle \frac{\Delta A}{A}$% $= 2 \displaystyle \left ( \frac{\Delta A}{r} \right ) \times 100$
$\displaystyle \frac{\Delta A}{A}$% $= 2 \times 0.15 = 0.30$%

If the volume of a sphere increases by 72.8%, then its surface area increases by

introduction to ratio and percentages comparing quantities maths

  1. 20%

  2. 44%

  3. 24.3%

  4. 48.6%

Show answer
Correct Option: B
Explanation:

$\displaystyle \frac{V'}{V} = \frac{172.8}{100} = \frac{\displaystyle \frac{4}{3} \pi R^{.3}}{\displaystyle \frac{4}{3} \pi R^3}$
$\displaystyle \frac{R'}{R} = 1.2$
Now, ratio of surface area $= \displaystyle \frac{S'}{S} = \frac{4 \pi R^{.2}}{4 \pi R^3}$
$= \displaystyle \frac{S'}{S} = 1.44$
Hence surface area increased by 44%

The given table shows the prices of 3 different types of eggs $\displaystyle \frac{1}{4}$ of the eggs Priyanka bought were chicken eggs $\displaystyle \frac{1}{8}$ of them were century eggs and the rest were quail eggs If Priyanka spent a total amount of Rs. 6.50 on the chicken and century eggs how much did she spent on the quail eggs? 

Chicken eggs 20 paise each
Century eggs 90 paise each
Quail eggs 5 paise each
introduction to ratio and percentages comparing quantities maths

  1. Rs. 1.25

  2. Rs. 1.40

  3. Rs. 1.65

  4. Rs. 1.80

Show answer
Correct Option: A
Explanation:

Let the total number of eggs=x.

So, number of chicken eggs= (1/4)*x
number of century eggs= (1/8)*x

number of quail eggs= total-(chicken eggs+century eggs)
$\begin{array}{c}x - \left( {\dfrac{1}{4}x + \dfrac{1}{8}x} \right) = x - \left( {\dfrac{3}{8}x} \right)\\ = \dfrac{5}{8}x\end{array}$
Cost of 1 chicken egg=20 paise
Cost of (1/4)*x chicken eggs= $\dfrac{1}{4} \times x \times 20 = 5x$
Cost of 1 century egg=90 paise
Cost of (1/8)*x chicken eggs= $\dfrac{1}{8} \times x \times 90 = 11.25x$
Cost of 1 quail egg=5 paise
Cost of (5/8)*x chicken eggs= $\dfrac{5}{8} \times x \times 5= 3.125x$

The total cost of chicken and century eggs=5x+11.25x
=16.25x

As for the cost of chicken and century eggs=Rs 6.5
So,
16.25x=6.5
x=0.4

Cost of quail eggs=3.125*x
=3.125*0.4
=1.25

Thus Option A


On selling $17$ balls at $Rs. 720$, there is a loss equal to the cost price of $5$ balls. The cost price of a ball is:

introduction to ratio and percentages comparing quantities maths

  1. $Rs. 45$

  2. $Rs. 50$

  3. $Rs. 55$

  4. $Rs. 60$

Show answer
Correct Option: D
Explanation:

$(C.P.\ of\ 17\ balls) - (S.P.\ of\ 17\ balls) = (C.P.\ of\ 5\ balls)$
$\Rightarrow$ C.P. of $12\ balls = S.P.\ of\ 17\ balls = Rs. 720$.
$\Rightarrow C.P.\ of\ 1\ ball = Rs. \left (\dfrac {720}{12}\right )= Rs. 60$.