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Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

Well-Grown potting soil is made from only peat moss and compost in a ratio of $3$ pounds of peat moss to $5$ pounds of compost. If a bag of Well-Grown potting soil contains $12$ pounds of potting soil, find how many pounds of peat moss it contains.

  1. $4.18$
  2. $4.22$
  3. $4.35$
  4. $4.50$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$3$ pounds of peat moss is to $5$ pounds of compost is the composition in $8$ pounds potting soil.

Since we have $12$ pounds of potting soil, corresponding amount of peat moss becomes $\cfrac{3 \times 12}{8} = 4.5 $ pounds

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

Two numbers are in the ratio of $1:2$. If $7$ be added to both, their ratio changes to $3:5$. The greater number is.

  1. $20$
  2. $24$
  3. $28$
  4. $32$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the numbers are $x$ and $y$ whose ratio is $1 : 2$

$\dfrac{x}{y}=\dfrac{1}{2}$
$\Rightarrow 2x=y$.......................................(1)
Given that when 7 added to both numbers, ratio changes to $3 : 5$
$\dfrac{x+7}{y+7}=\dfrac{3}{5}$
$\Rightarrow 5(x+7)=3(y+7)$
$\Rightarrow 5x+35=3y+21$
$\Rightarrow 5x-3y=21-35$
$\Rightarrow 5x-3y=-14$.................(2)
Put the value of $y=2x$ as per (1) we get
$5x-3(2x)=-14$
$5x-6x=-14$
$x=14$
Put the value of $x=14$ in (1) we get
$2\times 14=y$
$\Rightarrow y=28$
Then numbers are$ 14 ,28$
Then greater number is $28$.

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire rental of the car, then the share of each of the remaining persons increased by.

  1. $\dfrac{1}{9}$
  2. $\dfrac{1}{8}$
  3. $\dfrac{1}{7}$
  4. $\dfrac{7}{8}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Original share of 1 person $=\dfrac{1}{8}$
New share of 1 person $=\dfrac{1}{7}$

Then, share increased $=\dfrac{1}{7}-\dfrac{1}{8}=\dfrac{1}{56}$

So, required dfraction $=\dfrac{\dfrac{1}{56}}{\dfrac{1}{8}}=\dfrac{1}{56}\times \dfrac{8}{1}=\dfrac{1}{7}$
Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

$A, B$ and $C$ enter into partnership by making investments in the ratio $3:5:7$. After a year, $C $ invests another Rs. $337600$ while $A$ withdraws Rs. $45600$. The ratio of investments then changes to $24:59:167$. How much did $A$ invest initially?

  1. Rs. $45600$
  2. Rs. $96000$
  3. Rs. $141600$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial investments by $A, B$ and $C$ are $3x, 5x, 7x$

After a year:
$A$'s investment $=3x-45600$
$C$'s investment $=7x +337600$
$(3x-45600):5x : (7x+337600) = 24 : 59 : 167$
Solving this we will get $x=47200$
So, A's initial investment was $=3x = 3\times47200 = 141600$

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

Choose the correct answer from the alternatives given.
The ratio of length of two trains is 5 : 3 and the ratio of their speed is 6: 5. The ratio of time taken by them to cross a pole is

  1. $5 :6$
  2. $11:8$
  3. $25: 18$
  4. $27: 16$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

It is given that,
$\displaystyle \dfrac{l _1}{l _2} \, = \, \dfrac{5}{3} \, and \, \dfrac{s _1}{s _2} \, = \, \dfrac{6}{5} \, \Rightarrow \, \dfrac{t _1}{t _2} \, = \, \frac{s _1}{l _2} \, = \, \dfrac{l _1}{l _2} \, \times \, \dfrac{s _2}{s _1} \, = \, \dfrac{5}{3} \, \times \, \dfrac{5}{6} \, = \, \dfrac{25}{18}$
Hence, $t _1 : t _2$ = $25 : 18$

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

Choose the correct answer form the alternatives given.
The ratio of spirit and water in a mixture is 1: 3. If the volume of the solution is increased by 25% by adding spirit only. What is the resultant ratio of spirit and water? 

  1. $2:3$
  2. $1:4$
  3. $1: 2$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the volume of spirit and water be x and 3x Then, total volume = 4x. Resultant  volume of solution = 1.25 $\times$ 4x = 5x
Therefore, increase in volume = $5x - 4x = x$
So, the new ratio of spirit of water $2x : 3x = 2:3$
It is to be noted that increase in volume is due to addition of spirit only.

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

The expenses on wheat, meat and vegetables of a family are in the ratio 12: 17 : 3. The prices of these articles are increased by 20%, 30% and 50% respectively. The total expenses of the family on these articles are increased by

  1. 23$\frac{1}{3}$%
  2. 28$\frac{1}{8}$%
  3. 27$\frac{1}{8}$%
  4. 25$\frac{1}{7}$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given that expense on Wheat, Meat and Vegetable =12x + 17x + 3x = 32x
New expense on wheat, Meat and Vegetable
= 1.2 $\times 12x + 1.3 \times 17x + 1.5 \times 3x $
= 14.4x + 22.1x + 4.5x = 41x
Percentage increase in expense = $\frac{9}{32} \times 100 = 28\frac{1}{8}$%

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

The ratio  of number of boys and girls in a school of 720 students is 7 : 5 . How many more girls should be admitted to make the ratio 1 : 1 ?

  1. 100

  2. 120

  3. 80

  4. 150
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
The ratio of the number of boys to girls is $7:5$.
We make this part to part ratio to part to whole ratio by using the property
$a:b\displaystyle \Rightarrow \dfrac{a}{a+b}:\dfrac{b}{a+b}$
$\displaystyle \therefore $ Ratio of the boys to the total students
=$\displaystyle \dfrac{7}{7+5}=\dfrac{7}{12}$
and the ratio of the girls to the total students
$\displaystyle \dfrac{5}{7+5}=\dfrac{5}{12}$
To get the answer we would first find out the actual number of boys and girls in the school
For this we multiply the total number with their respective ratios
$\displaystyle \therefore $ Number of boys=$\displaystyle \dfrac{7}{12}\times 720=7\times 60=420$
and Number of girls=$\displaystyle \dfrac{5}{12}\times 720=5\times 60=300$
Now we need to obtain the boys to girls ratio as 1:1 For this the number of boys and girls should be equal This can be obtained by adding $420-300=120$ girls in the school
Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

Two-third of one-seventh of a number is $87.5$% of $240$. What is the number?

  1. $2670$
  2. $2450$
  3. $2205$
  4. $1470$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $\dfrac {2}{3}$ of $\dfrac {1}{7}$ of a number say $x$ is $87.5\%$ of $240$.

$\therefore \displaystyle \frac{2}{3}\times\frac{1}{7}\times x=\frac{87.5}{100}\times240$

$\displaystyle \Rightarrow x =\frac{87.5\times240\times3\times7}{2\times100}=2205$
therefore, the number is $2205$.