Two numbers are in the ratio 2 : 5. If 16 is added to both the numbers, their ratio becomes 1 : 2. The numbers are:
32, 80
Let's solve the problem step-by-step to find the actual numbers based on the provided ratios.
- Let the two numbers be \(2x\) and \(5x\) because they are in the ratio \(2:5\).
- According to the problem, if 16 is added to both numbers, the new ratio becomes \(1:2\). So, we can write this as:
\(\frac{2x + 16}{5x + 16} = \frac{1}{2}\) - To solve this equation, we cross-multiply:
\(2(2x + 16) = 1(5x + 16)\) - Expanding both sides,
\(4x + 32 = 5x + 16\) - Rearranging the terms gives:
\(32 - 16 = 5x - 4x\)
\(16 = x\) - Now we have \(x = 16\).
- So the original numbers are:
\(2x = 2 \times 16 = 32\)
\(5x = 5 \times 16 = 80\)
Therefore, the two numbers are 32 and 80.
Let's verify this solution:
- Original numbers: 32 and 80.
- After adding 16, the numbers become 48 and 96 respectively.
- New ratio is \(\frac{48}{96} = \frac{1}{2}\), which matches the condition given in the problem.
This confirms that the correct answer is indeed 32 and 80.
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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.)
- 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 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?
