Tag: mathematical logic

Questions Related to 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?

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

The conditional $( p \wedge q ) \Rightarrow p$ is 

maths mathematical reasoning special words/phrases duality mathematical logic

  1. neither tautology nor contradiction

  2. a tautology

  3. a contradiction

  4. both tautology and contradiction

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Correct Option: B

Boolean algebra is also called

maths mathematical reasoning special words/phrases duality mathematical logic

  1. switching algebra

  2. arithmetic algebra

  3. linear algebra

  4. algebra

Show answer
Correct Option: A
Explanation:

Boolean algebra is also called switching algebra..


It was invented by mathematician George Boole in 1849.Boolean algebra or 

switching algebra ia a system of mathematical logic to perform different 

mathematical operation in binary system.

$e*x=x*e=x$ is the

maths mathematical reasoning special words/phrases duality mathematical logic

  1. commutative property

  2. inverse property

  3. associative property

  4. identity element

Show answer
Correct Option: D
Explanation:

Given, $e\times x=x\times e=x$

This is possible when $e=1$
This is an identity element.

A Boolean function may be transformed into

maths mathematical reasoning special words/phrases duality mathematical logic

  1. logical diagram

  2. logical graph

  3. map

  4. matrix

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Correct Option: A
Explanation:

Boolean function:

        It can be represented in the form of diagram with logic gates.

Boolean algebra theorem, gives   $x\cdot (x+y)$   equal to

maths mathematical reasoning special words/phrases duality mathematical logic

  1. $x'$

  2. $1$

  3. $x$

  4. $0$

Show answer
Correct Option: C
Explanation:

    $x\cdot \left( x+y \right) $

$=x\cdot x+xy$
$=x$