Finding the Original Number
Let the original number be represented by the variable \(x\). The problem states that when one-third of this number is increased by 83, the result is 97.
We can write this as an equation:
\( \frac{1}{3}x + 83 = 97 \)To solve for \(x\), first subtract 83 from both sides:
\( \frac{1}{3}x = 97 - 83 \) \( \frac{1}{3}x = 14 \)Now, multiply both sides by 3 to find the value of \(x\):
\( x = 14 \times 3 \) \( x = 42 \)So, the original number is 42.
Calculating the Sum of Digits
The question asks for the sum of the digits of the original number (which is 42).
The digits are 4 and 2.
Sum of digits = \(4 + 2 = 6\).
The sum of the digits of the original number is 6.
Similar Questions
The value of (x - y)(x + y) + (y - z)(y + z) + (z - x)(z + x) is:
- For what value of K is the equation \(\frac{0.009}{K} = 0.1\) true?
- Arnab buys 9 oranges and 8 bananas for ₹276. When the cost of an orange is decreased by 10% and that of a banana remains the same, then the cost of 5 oranges and 10 bananas is ₹210. What is the original cost of 4 oranges and 3 bananas?
- If a + b = 7 and ab = 12, then \(a^2 + b^2\) is equal to:
Reduce to linear form
\(\frac{5x + 1}{2x} = \frac{5}{4}\)
What is the product of (x + a) and (x + b)?
A 3-digit number is such that the units' digit, the tens' digit, and the hundreds' digit are in the ratio 1 : 2 : 3. The sum of this number and the number obtained by writing its digits in reverse order is 1332. Find the number.
- If \(a^2 + b^2 + c^2 + 189 = 6(a + 4b + 2c)\), then \(\sqrt{ab + bc + ca}\) is equal to:
A fraction becomes \(1\over2\) if 2 is added to the numerator and 5 is added to the denominator. It also becomes \(1\over 3\) if 2 is subtracted from both the numerator and denominator. The positive difference between the numerator and the denominator is:
The cost of 12 pens and 7 pencils is ₹233. If the cost of a pen decreases by ₹1.50 and the cost of a pencil increases by ₹1, then the cost of 2 pens and 3 pencils is ₹48. What is the original cost of 2 pens and 3 pencils?
Important Questions from Algebric Equations
A group of 630 children is seated in rows for a group photo session. Each row contains three less children than the row in front of it. Which one of the following number of rows is not possible?
The letters L, M, N, 0, P, Q, R, S and T in their order are substituted by nine integers 1 to 9 but not in that order. 4 is assigned to P. The difference between P and T is 5. The difference between N and T is 3.
What is the integer assigned to N?
Four persons, Alok, Bhupesh, Chander and Dinesh have a total of Rs. 100 among themselves. Alok and Bhupesh between them have as much money as Chander and Dinesh between them, but Alok has more money than Bhupesh; and Chander has only half the money that Dinesh has. Alok has in fact Rs. 5 more than Dinesh has.
Who has the maximum amount of money?
If x=3/2, then the value of 27x3-54x2+36x-11 is
If a+b+c = 6 and ab+bc+ca = 11, then the value of bc(b+c) + ca(c+a) +ab(a+b) +3abc is
