Question
Three numbers are in the ratio 19:21:23. If the difference between thrice the third number and the sum of first and second number is 841. Find the difference between the first and third number?
The correct answer is
116
Ratio Numbers Calculation
Let the three numbers be represented based on the given ratio $19:21:23$. We can denote these numbers as $19x$, $21x$, and $23x$, where $x$ is a common multiplier.
Condition Analysis
The problem states that the difference between thrice the third number and the sum of the first and second number is 841.
- Third number = $23x$
- First number = $19x$
- Second number = $21x$
- Sum of first and second = $19x + 21x = 40x$
- Thrice the third number = $3 \times 23x = 69x$
Translating the condition into an equation:
$69x - 40x = 841$Solving for the Multiplier (x)
Simplify the equation:
$29x = 841$Solve for $x$:
$x = \frac{841}{29}$ $x = 29$Finding the Difference
We need to find the difference between the first and third numbers.
- First number = $19x$
- Third number = $23x$
- Difference = Third number - First number
- Difference = $23x - 19x$
- Difference = $4x$
Substitute the value of $x$ found:
$ \text{Difference} = 4 \times 29 $ $ \text{Difference} = 116 $Final Answer Determination
The difference between the first and third number is 116.
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Important Questions from Ratio and Proportion
- A box containing the denominations of one rupee coins, five rupee coins and ten rupee coins amount to Rs.4320. There are equal number of
coins in all denominations. What is the total number of coins in the box? - The sum of three terms is 14380. The ratio between first term and second term is 14:15 and the ratio between second term and the third term is 16:17. Find the difference between first and last term.
- A box containing the denominations of fifty paise coins, two rupee coins and five rupee coins amount to Rs. 1275. There are equal number of coins in all denominations. What is the value of two rupee coins in the box? (In Rs.)
- The ratio between the number of males and females in a college is 27:28. If the number of males are increased by 20% and the number of females are increased by 30%, then what will the new ratio of males and females in the college?
- A box containing the denominations of one rupee coins, two rupee coins and ten rupee coins amount to Rs.2730. There are equal number of coins in all denominations. What is the total number of one rupee coins in the box?
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