Tag: maths

Questions Related to maths

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.

maths mixture types of ratios ratios in proportion mathematical logic

  1. $4.18$

  2. $4.22$

  3. $4.35$

  4. $4.50$

Show answer
Correct Option: D
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

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.

maths mixture types of ratios ratios in proportion mathematical logic

  1. $20$

  2. $24$

  3. $28$

  4. $32$

Show answer
Correct Option: C
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 $28$.

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.

maths mixture types of ratios ratios in proportion mathematical logic

  1. $\dfrac{1}{9}$

  2. $\dfrac{1}{8}$

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

  4. $\dfrac{7}{8}$

Show answer
Correct Option: C
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 $=\dfrac{\dfrac{1}{56}}{\dfrac{1}{8}}=\dfrac{1}{56}\times \dfrac{8}{1}=\dfrac{1}{7}$

$A, B$ 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?

maths mixture types of ratios ratios in proportion mathematical logic

  1. Rs. $45600$

  2. Rs. $96000$

  3. Rs. $141600$

  4. None of these

Show answer
Correct Option: C
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 $=3x = 3\times47200 = 141600$

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

maths mixture types of ratios ratios in proportion mathematical logic

  1. $5 :6$

  2. $11:8$

  3. $25: 18$

  4. $27: 16$

Show answer
Correct Option: C
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, $t _1 : t _2$ = $25 : 18$

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? 

maths mixture types of ratios ratios in proportion mathematical logic

  1. $2:3$

  2. $1:4$

  3. $1: 2$

  4. None of these

Show answer
Correct Option: A
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.

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

maths mixture types of ratios ratios in proportion mathematical logic

  1. 23$\frac{1}{3}$%

  2. 28$\frac{1}{8}$%

  3. 27$\frac{1}{8}$%

  4. 25$\frac{1}{7}$%

Show answer
Correct Option: B
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 = $\frac{9}{32} \times 100 = 28\frac{1}{8}$%

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 ?

maths mixture types of ratios ratios in proportion mathematical logic

  1. 100

  2. 120

  3. 80

  4. 150

Show answer
Correct Option: B
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

$120\%$ of $45$

maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

  1. $45$

  2. $54$

  3. $34$

  4. $43$

Show answer
Correct Option: B
Explanation:
Given,

$120\%$ of $45$

$=\dfrac{120}{100} \times 45$

$=\dfrac{12}{2} \times 9$

$=6 \times 9$

$=54$

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

maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

  1. $2670$

  2. $2450$

  3. $2205$

  4. $1470$

Show answer
Correct Option: C
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 $2205$.