Tag: ratios in proportion

Questions Related to ratios in proportion

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

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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$\frac{1}{7}$%

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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