Finding the Number Equidistant from 75 and 117
The problem asks for a number that is the same distance away from 75 as it is from 117. This means the number is exactly in the middle of 75 and 117.
Method 1: Using Algebra
- Let the unknown number be $x$.
- According to the problem, the number is as much greater than 75 as it is smaller than 117. We can write this as an equation: $x - 75 = 117 - x$
- To solve for $x$, first add $x$ to both sides: $x + x - 75 = 117 - x + x$ $2x - 75 = 117$
- Next, add 75 to both sides: $2x - 75 + 75 = 117 + 75$ $2x = 192$
- Finally, divide by 2: $x = \frac{192}{2}$ $x = 96$
Method 2: Calculating the Average
The number that is exactly in the middle of two other numbers is their average (mean).
- Add the two given numbers: $75 + 117 = 192$.
- Divide the sum by 2 to find the average: $\frac{192}{2} = 96$.
Both methods show that the number is 96.
Check: Is 96 greater than 75 by the same amount it is smaller than 117? Difference 1: $96 - 75 = 21$ Difference 2: $117 - 96 = 21$ The differences are equal, confirming the answer.
The number is 96.
Important Questions from Numerical Computation
- An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20% of the consulting fee, if the fee is up to . 5,00,000. For higher fees, the overhead is . 1,00,000 plus 10% of the amount by which the fee exceeds . 5,00,000. The government charges a Goods and Services Tax of 18% on the total amount (the consulting fee plus the overhead). An employee of the organization charges this entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client cannot pay more than . 10,00,000, what is the maximum consulting fee that the employee can charge?
Three frictionless pulleys with rope attachment are in a static equilibrium as shown in the figure. The mass $m_1$ and $m_2$, in kg, respectively are
If the in-situ density of coal is 1320 kg/m$^3$ and the density of blasted coal is 952 kg/m$^3$, the swell factor is _____________ (rounded off to 3 decimal places)
A five-member truss system is shown in the figure. The maximum vertical force P in kN that can be applied so that loads on the member CD and BC do NOT exceed 50 kN and 30 kN, respectively is _____________(rounded off to 2 decimal places)
The Fourier transform and its inverse transform are respectively defined as $\tilde{f}(\omega) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} f(x)e^{i\omega x}dx$ and $f(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} \tilde{f}(\omega)e^{-i\omega x}d\omega$. Consider two functions $f$ and $g$. Another function $f * g$ is defined as
$(f * g)(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} f(y)g(x - y)dy$
Which of the following relation is/are true?
Note: Tilde ($\sim$) denotes the Fourier transform.
