Tag: comparing quantities

Questions Related to comparing quantities

A man saves 20% of his monthly salary. If on account of increase in prices, he is to increase his monthly expenses by 20%, he is only able to save Rs 800 per month. His monthly salary is

introduction to ratio and percentages comparing quantities maths

  1. Rs 40,000

  2. Rs 28,000

  3. Rs 24,000

  4. Rs 20,000

Show answer
Correct Option: D
Explanation:

Let the salary be Rs 100
Savings $=$ Rs 20 ; Expenditure $=$ Rs 80
New expenditure $=$ 120% of Rs 80 $=$ Rs 96.
New savings $=Rs:100-Rs:96=Rs:4$
$\implies4\%x=Rs:800\implies x=Rs:20,000$

Alfred buys an old scooter for Rs. $4700$ and spends Rs. $800$ on its repairs. If he sells the scooter for Rs. $5800$, his gain percent is:

introduction to ratio and percentages comparing quantities maths

  1. $4\dfrac {4}{7}$%

  2. $5\dfrac {5}{11}$%

  3. $10$%

  4. $12$%

Show answer
Correct Option: B
Explanation:

Cost Price $(C.P.) = Rs. (4700 + 800) = Rs. 5500$.
Selling Price $(S.P.) = Rs. 5800$.
$Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300$.
Gain % $= \left (\dfrac {300}{5500}\times 100\right )$% $= 5\dfrac {5}{11}$%

If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?

introduction to ratio and percentages comparing quantities maths

  1. 48 paise

  2. 54 paise

  3. 56 paise

  4. 72 paise

Show answer
Correct Option: A
Explanation:

Let the required weight be x kg.
Less weight, Less cost (Direct Proportion)
$\therefore 250 : 200 :: 60 : x \Leftrightarrow 250 \times x = (200 \times 60)$
$\Rightarrow x = \dfrac{(200 \times 60)}{250}$
$\Rightarrow x = 48$

A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions mad by the larger wheel is

introduction to ratio and percentages comparing quantities maths

  1. 4

  2. 9

  3. 12

  4. 49

Show answer
Correct Option: B
Explanation:

Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
$\therefore 14 : 6 :: 21 : x \Leftrightarrow 14 \times x = 6 \times 21$
$\Rightarrow x = \dfrac{6 \times 21}{14}$
$\Rightarrow x = 9$

A flagstaff 17.5 m high casts a shadow of length 40.25 m. The height of the building, which casts a shadow of length 28.75 m under similar conditions will be

introduction to ratio and percentages comparing quantities maths

  1. 10 m

  2. 12.5 m

  3. 17.5

  4. 21.25 m

Show answer
Correct Option: B
Explanation:

Let the height of the building x metres.
Less lengthy shadow, Less in the height (Direct Proportion)
$\therefore 40.25 : 28.75 :: 17.5 : x \Leftrightarrow 40.25 \times x = 28.75 \times 17.5$
$x = \dfrac{28.75 \times 17.5}{40.25}$
$\Rightarrow x = 12.5$

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