Tag: comparing quantities

Questions Related to comparing quantities

6 dozen eggs are bought for Rs. 48. How much will 132 eggs cost ?

introduction to ratio and percentages comparing quantities maths

  1. Rs. 78

  2. Rs. 80

  3. Rs. 82

  4. Rs. 88

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Correct Option: D
Explanation:

6 dozen eggs = 72 eggs
Let the required amount be Rs. x.

Now,
$72:132::48:x$
$\dfrac{72}{132}=\dfrac{48}{x}$

$x=88$
Therefore,
Required amount = $Rs. 88$

The food stocks in a hostel are sufficient for 1200 students for 20 days . If 400 more students joined the hostel , the stocks just for ... days .

introduction to ratio and percentages comparing quantities maths

  1. 12

  2. 15

  3. 18

  4. 21

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Correct Option: B
Explanation:

Let food stock is sufficient for $x$ days.

Given,
$M _{1}=1200$
$D _{1}=20$
$M _{2}=1200+400=1600$
$D _{2}=x$
Then, using $M _{1}D _{1}=M _{2}D _{2}$
$1200\times 20 = 1600\times x$
$x=\dfrac{1200\times 20}{1600}$
$x=15$
Therefore, now the food stock is sufficient for $15$ days.

The time taken (in hours) by a car to travel $900km$ if it travels $600 km $ in $12 hrs$.

introduction to ratio and percentages comparing quantities maths

  1. 18

  2. 16

  3. 15

  4. None of these

Show answer
Correct Option: A
Explanation:

Time taken to cover $600km$ is `12 Hrs

Speed of car is given as $\dfrac{600}{12}=50kmph$
Time taken to cover $900km$ is $\dfrac{900}{50}=18hrs$

If 10% of x=20% of y, then $x:y$ is equal to

introduction to ratio and percentages comparing quantities maths

  1. $1:2$

  2. $2:1$

  3. $5:1$

  4. $10:1$

Show answer
Correct Option: B
Explanation:
Given,

$10$% $x$ = $20$% $y$

$\dfrac{x}{y}=\dfrac{20}{10}$%

$\therefore x:y=2:1$

$33\dfrac { 1 }{ 3 } %\quad of\quad 1\dfrac { 1 }{ 2 } $ minute is equal to ___

introduction to ratio and percentages comparing quantities maths

  1. 2000 seconds

  2. 5000 seconds

  3. 3000 seconds

  4. 6000 seconds

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Correct Option: A
Explanation:
$1$minute$=60$seconds
$33\dfrac{1}{3}$ minutes$=33\dfrac{1}{3}\times 60$ seconds
$=\dfrac{100}{3}\times 60$ seconds
$=100\times 20$ seconds
$=2000$seconds.

What is the sum of two numbers?
I. The bigger of these two numbers is 6 more than the smaller number.
II. 40% of the smaller number is equal to 30% of the bigger number.
III. The ratio between half of the bigger number and one-third of the smaller number is 2 : 1

introduction to ratio and percentages comparing quantities maths

  1. Only II and III are sufficient

  2. Only I and II are sufficient

  3. I and either II or III is sufficient

  4. All, II and III together are sufficient

Show answer
Correct Option: C
Explanation:

From the given statements we can make the following equations.
(I) $\Rightarrow y=x+6$
(II) $\Rightarrow 0.4x=0.2y\Rightarrow \frac {x}{y}=\frac {x}{y}=\frac {3}{4}$
(III) $\Rightarrow \frac {y/2}{x/3}=\frac {2}{1}\Rightarrow \frac {y}{x}=\frac {4}{3}\Rightarrow \frac {x}{y}=\frac {3}{4}$
Obviously, question can be solved by using (I) and either (II) or (III) because equations (II) and (III) are same.

The difference between simple interest and compound interest on a certain sum of money for 3 years at 5% per annum is Rs. 122. Find the sum

introduction to ratio and percentages comparing quantities maths

  1. Rs. 12,200

  2. Rs. 15,000

  3. Rs. 16,500

  4. Rs. 16,000

Show answer
Correct Option: D
Explanation:

Suppose $sum=P$
Given $CI-SI=Rs. 122$
$P\left (1+\frac {5}{100}\right )^3-P-\left (\frac {P\times 5\times 3}{100}\right )=122$
$P\left (\frac {105^3}{100^3}-1-\frac {15}{100}\right )=122$
$P\left (\frac {7,625}{100^3}\right )=122$
$P=\frac {122\times 100^3}{7,625}=Rs. 16,000$

Two cats Billy and Kitty together catch 60 mice. If Billy catches three mice for every two caught by Kitty, the number of mice caught by Kitty is

introduction to ratio and percentages comparing quantities maths

  1. 24

  2. 30

  3. 36

  4. 40

Show answer
Correct Option: A
Explanation:

Ratio of catches by Billy and Kitty is 3 : 2. Therefore,
$3x+2x=60$
$5x=60$ or $x=\frac {60}{5}=12$
Number of mice caught by Kitty $=2x=2\times 12=24$

A person spent Rs 564 in buying geese and ducks. If each goose costs Rs 7, each duck Rs 3, and if the total number of birds bought was 108, how many of each did he buy?

introduction to ratio and percentages comparing quantities maths

  1. 60 and 48

  2. 48 and 36

  3. 48 and 24

  4. 60 and 30

Show answer
Correct Option: A
Explanation:

In questions of this kind, it is essential to have all quantities expressed in the same denomination; in the present instance, it will be convenient to express the money in rupees.
Let x be the number of geese. Then 108 -x is the number of ducks.
Since each goose costs 7 rupees, x geese cost 7x rupees.
And since each duck costs 3 rupees, 108 -x ducks cost 3(108 -x) rupees.
Therefore, the amount spent is 7x + 3(108 -x) rupees; but the question states that the amount is Rs 564. Hence,
$7x + 3(108 -x) = 564$
or $7x + 324 -3x = 564$
or $4x = 240$
Therefore, the number of geese, $x = 60$, and the number of ducks, $108 -x = 48$.

A person invested Rs 1,600 for 3 years and Rs 1,100 for 4 years at the same rate of simple interest. The total interest from these investments was Rs 506. Find the rate percent per annum

introduction to ratio and percentages comparing quantities maths

  1. 5%

  2. $5\frac {1}{2}$%

  3. 6%

  4. $6\frac {1}{2}$%

Show answer
Correct Option: B
Explanation:

$P _1=1,600, t _1=3$
$P _2=1,1000, t _2=4$
$SI _1+SI _2=506$
or $\frac {1,600\times 3\times r}{100}+\frac {1,100\times 4\times r}{100}=506$
or $r(4,800+4,400)=506\times 100$
or $r=\frac {506\times 100}{92,000}=5.5$%