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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The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
