Speed Mathematics Overview

Speed Mathematics Overview

Introduction

Once you understand the chapters in these tutorials of speed mathematics, you will be able to solve complex mathematical calculations very fast and accurately. You can do these complex mathematical problems mentally.

The principles in these tutorials are taken from various systems like Indian Vedic Mathematics and the German Trachtenberg System.

Vedic Mathematics

Vedic Mathematics is the ancient system of Indian Mathematics. It is originated from "Atharva Vedas", the fourth Veda. This wonderful method is reintroduced to the world by Swami Bharati Krisna Tirtha ji Mahaharaj The book Vedic Mathematics was written by Jagadguru Swami Sri Bharati Krishna Tirthaji Maharaja. He describes Vedic Mathematics as a system of mental calculation.

In Vedic Mathematics, huge problems can be solved very easily and quickly. This is the beauty of it. Vedic Mathematics uses a very simple system. The calculation strategies provided by Vedic mathematics are very powerful and can be applied to various calculation methods in arithmetic and algebra.

The tutorials in this section makes you aware how powerful this system is. Once you learn this system, you can solve big mathematical problems mentally

Trachtenberg System of Mathematics

Jakow Trachtenberg created the Trachtenberg system of mathematics. It is system of quick mental calculation. Researches indicates that the system reduces the time for mathematical operations up to a good extent. Trachtenberg system is not only speedy, but accurate and simple.

Quant Quiz

Problems on Age - Solved Examples (Set 6)

26. The product of the ages of Syam and Sunil is $240$. If twice the age of Sunil is more than Syam's age by $4$ years, what is Sunil's age?
A. $16$	B. $14$
C. $12$	D. $10$

answer with explanation

Answer: Option C
Explanation:
Let age of Sunil $=x$ and
age of Syam $=y$

$xy=240\cdots \left(1\right)$

$2x=y+4\Rightarrow y=2x-4\Rightarrow y=2(x-2)\cdots \left(2\right)$

Substituting equation $\left(2\right)$ in equation $\left(1\right)$. We get
$x\times 2(x-2)=240\Rightarrow x(x-2)=\frac{240}{2}\Rightarrow x(x-2)=120\cdots \left(3\right)$

We got a quadratic equation to solve.

Always time is precious and objective tests measure not only how accurate you are but also how fast you are. We can solve this quadratic equation in the traditional way. But it is more easy to substitute the values given in the choices in the quadratic equation (equation $3$) and see which choice satisfy the equation.

Here, option A is $10$. If we substitute that value in the quadratic equation, $x(x-2)=10\times 8$ which is not equal to $120$

Now try option B which is $12$. If we substitute that value in the quadratic equation, $x(x-2)=12\times 10=120$. See, we got that $x=12$

Hence Sunil's age $=12$

(Or else, we can solve the quadratic equation by factorization as,
$x(x-2)=120\Rightarrow x^2-2x-120=0\Rightarrow (x-12)(x+10)=0\Rightarrow x=12\text{or}-10$
Since $x$ is age and cannot be negative, $x=12$

Or by using quadratic formula as
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{2\pm \sqrt{(-2{)}^2-4\times 1\times (-120)}}{2\times 1}=\frac{2\pm \sqrt{4+480}}{2}=\frac{2\pm \sqrt{484}}{2}=\frac{2\pm 22}{2}=12\text{or}-10$

Since age is positive, $x=12$

27. One year ago, the ratio of Sooraj's and Vimal's age was $6:7$ respectively. Four years hence, this ratio would become $7:8$. How old is Vimal?
A. $32$	B. $34$
C. $36$	D. $38$

answer with explanation

Answer: Option C
Explanation:
Let the age of Sooraj and Vimal, $1$ year ago, be $6x$ and $7x$ respectively.

Given that, four years hence, this ratio would become $7:8$
$\Rightarrow (6x+5):(7x+5)=7:8\Rightarrow 8(6x+5)=7(7x+5)\Rightarrow 48x+40=49x+35\Rightarrow x=5$

Vimal's present age
$=7x+1=7\times 5+1=36$

28. The total age of A and B is $12$ years more than the total age of B and C. C is how many year younger than A?
A. $10$	B. $11$
C. $12$	D. $13$

answer with explanation

Answer: Option C
Explanation:
Solution 1

Given that, A + B $=12+$ B + C
⇒ A - C $=12$
Therefore, C is younger than A by $12$ years

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Solution 2

Total age of A and B is $12$ years more than total age of B and C.

Since B is common in both sides, C is $12$ years younger than A.

29. Sachin's age after $15$ years will be $5$ times his age $5$ years back. Find out the present age of Sachin?
A. $10$ years	B. $11$ years
C. $12$ years	D. $13$ years

answer with explanation

Answer: Option A
Explanation:
Let present age of Sachin $=x.$ Then,

$(x+15)=5(x-5)\Rightarrow 4x=40\Rightarrow x=10$

30. Sandeep's age after six years will be three-seventh of his father's age. Ten years ago the ratio of their ages was $1:5$. What is Sandeep's father's age at present?
A. $30$ years	B. $40$ years
C. $50$ years	D. $60$ years

answer with explanation

Answer: Option C
Explanation:
Let the age of Sandeep and his father before $10$ years be $x$ and $5x$ respectively.

Given that Sandeep's age after six years will be three-seventh of his father's age
$\Rightarrow x+16=\frac{3}{7}(5x+16)\Rightarrow 7x+112=15x+48\Rightarrow 8x=64\Rightarrow x=8$

Sandeep's father's present age
$=5x+10=5\times 8+10=50$