Tag: introduction to ratio and percentages

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Multiple choice introduction to ratio and percentages comparing quantities maths

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

  1. Rs 40,000

  2. Rs 28,000

  3. Rs 24,000

  4. Rs 20,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

Multiple choice introduction to ratio and percentages comparing quantities maths

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:

  1. $4\dfrac {4}{7}$%
  2. $5\dfrac {5}{11}$%
  3. $10$%
  4. $12$%
Reveal answer Fill a bubble to check yourself
B Correct answer
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 % $= \left (\dfrac {300}{5500}\times 100\right )$% $= 5\dfrac {5}{11}$%

Multiple choice introduction to ratio and percentages comparing quantities maths

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

  1. 48 paise

  2. 54 paise

  3. 56 paise

  4. 72 paise
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

Multiple choice introduction to ratio and percentages comparing quantities maths

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

  1. 4

  2. 9

  3. 12

  4. 49
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

Multiple choice introduction to ratio and percentages comparing quantities maths

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

  1. 10 m

  2. 12.5 m

  3. 17.5

  4. 21.25 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

Multiple choice introduction to ratio and percentages comparing quantities maths

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

  1. 12

  2. 18

  3. 22

  4. 24

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

Multiple choice introduction to ratio and percentages comparing quantities maths

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

  1. 1
  2. $\dfrac{7}{2}$

  3. 7

  4. 49
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

Multiple choice introduction to ratio and percentages comparing quantities maths

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?

  1. $7$ hours $30$ minutes
  2. $8$ hours
  3. $8$ hours $15$ minutes
  4. $8$ hours $25$ minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

Multiple choice introduction to ratio and percentages comparing quantities maths

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:

  1. $15$
  2. $16$
  3. $18$
  4. $25$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

Multiple choice introduction to ratio and percentages comparing quantities maths

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:

  1. $61.75$
  2. $67.25$
  3. $82.33$
  4. $Data\ insufficient$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The product of the four numbers is 9261000. If we assume the numbers are equal or near each other, the cube root of 9261000 is 210. However, the question states each number is formed by 3 distinct prime numbers. This implies a specific set of numbers. Given the options, 61.75 is the only plausible arithmetic mean.