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
$A$ is an ($n \times n$) matrix. Consider the following two statements
Statement 1: Columns of matrix $A$ are linearly independent
Statement 2: Inverse of matrix $A$ exists
Which one of the following statements is TRUE?
- Consider the function $G(x, y, z) = 0$. This function allows us to implicitly define each of three variables as a function of the other two variables. Assume that all partial derivatives of the function $G(x, y, z)$ exist everywhere. Then, the value of $\left(\frac{\partial z}{\partial x} \times \frac{\partial x}{\partial y} \times \frac{\partial y}{\partial z}\right)$ is _________ (in integer)
- Levenshtein distance is used to measure the minimum edit distance between two strings by counting the minimum number of editing operations (such as, insertions, deletions, substitutions) required to transform one string to another. Consider an alternative version of the Levenshtein distance in which each insertion and each deletion has a cost of 1 and substitutions are not allowed.
Based on this alternative version, the Levenshtein distance between the strings, word and work is ______ (Answer in integer). - In a given collection of documents, let $N$ be the total number of documents and let $d$ be the number of documents in which the term $t$ occurs.
Which ONE of the following fractions is used to define the inverse document frequency (idf) of the term $t$? - The total number of unique character bigrams in the string thoughtsoftheghosts (which contains 19 characters) is ______.
