Gift Cost Calculation Using Algebra
This problem involves calculating the total cost of a gift based on a shared contribution that changes when some contributors withdraw.
Initial Situation Analysis
Ten friends initially planned to share the cost of a gift equally. Let the total cost of the gift be denoted by $C$.
The initial number of friends is 10.
The share per friend initially would be: $ \text{Initial Share} = \frac{C}{10} $
Revised Contribution Scenario
Two friends decided not to contribute. This leaves $10 - 2 = 8$ friends to share the cost.
The new share per contributing friend is: $ \text{New Share} = \frac{C}{8} $
Calculating the Extra Cost
Each of the remaining friends had to pay Rs 150 more than their initial planned share. This gives us the equation:
$ \text{New Share} - \text{Initial Share} = 150 $Substituting the expressions for the shares:
$ \frac{C}{8} - \frac{C}{10} = 150 $Solving for the Gift Cost
To solve for $C$, we first find a common denominator for 8 and 10, which is 40.
- Rewrite the fractions with the common denominator: $ \frac{5C}{40} - \frac{4C}{40} = 150 $
- Combine the fractions: $ \frac{5C - 4C}{40} = 150 $ $ \frac{C}{40} = 150 $
- Isolate $C$ by multiplying both sides by 40: $ C = 150 \times 40 $ $ C = 6000 $
Therefore, the total cost of the gift was Rs 6000.
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.
