Analyzing the Travel Expenses Problem
This problem involves calculating an initial budget based on changes in average daily expenses due to an extended stay. We need to find the total amount sanctioned to Sonal.
Setting Up the Equations
Let the total amount sanctioned (budget) be B.
- Initial duration = 16 days.
- Initial average daily allowance = $\frac{B}{16}$.
- Extended duration = 16 days + 8 days = 24 days.
- New average daily allowance = $\frac{B}{24}$.
- The difference in average daily allowance is given as ₹80.
Calculating the Initial Sanctioned Amount
- Set up the equation based on the difference in average daily allowance:
$ \frac{B}{16} - \frac{B}{24} = 80 $
- Find a common denominator for the fractions (which is 48):
$ B \left( \frac{1}{16} - \frac{1}{24} \right) = 80 $
$ B \left( \frac{3}{48} - \frac{2}{48} \right) = 80 $
- Simplify the expression:
$ B \left( \frac{1}{48} \right) = 80 $
- Solve for B (the total sanctioned amount):
$ B = 80 \times 48 $
$ B = 3840 $
Therefore, the initial amount sanctioned to Sonal was ₹3,840.
Similar Questions
- Find the value of x satisfying: $2(3x^2 - 7) - 3(2x^2 + 7x - 9) = 13$
- If $(1 + 2 + \text{x}) - (0.12 - 0.42 + 0.94) = 4$, then what will be the value of x?
- Find the value of x satisfying: $5(5x^2 - 6) - 5(5x^2 + 2x - 4) = 20$
- The sum of half, one-third and one-fifth of a number exceeds the number by $12$. What is the number?
- Anushka has kept four erasers, some pencils and some sharpeners in a bag. The number of sharpeners is one-fourth of the number of pencils. How many pencils does she have, if the total number of the three items is 49?
- Find the value of x.
$6(8x + 25) - 70 = 5(8x + 25)$ - If $11 = \frac{11x}{1 - x}$, then the value of $(2x)^2$ is:
- Find the number whose four-fifth is more than its three-fourth by 4.
- When 38 is added to $30\%$ of a number. The result is 50. What is the number?
- Find the value of $x$.
$6(8 x+25)-70=5(8 x+25)$
Important Questions from Linear Equation in 1 Variable
The sum of three fractions A, B, and C, A > B > C, is \(\frac{121}{60}\) . When C is divided by B, the resulting fraction is \(\frac{9}{10}\) , which exceeds A by \(\frac{3}{20}\) . What is the difference between B and C?
7 is added to a certain number and the sum is multiplied by 5. The product is then divided by 3 and 4 is subtracted from the quotient. If the result comes to 16, then what is the original number?
If the measure of one angle of a right triangle is 30° more than the measure of the smallest angle, then the measure of the smallest angle is:
A man has equal number of five, ten and twenty rupee notes amounting to Rs. 385. Find the total number of notes?
The sum of three consecutive number is 126. Find the highest number?
