What should be subtracted from 7, 9, 8, 11 so that the remaining numbers may be proportional?
5
Let \(x\) be subtracted from each. For the resulting numbers to be in proportion:
\((7 - x) : (9 - x) :: (8 - x) : (11 - x)\)
Cross-multiply:
\((7 - x)(11 - x) = (9 - x)(8 - x)\)
Expand both sides:
\(77 - 18x + x^{2} = 72 - 17x + x^{2}\)
Simplify (the \(x^{2}\) terms cancel):
\(77 - 18x = 72 - 17x \quad \Rightarrow \quad 5 = x\)
Verify: 7−5, 9−5, 8−5, 11−5 = 2, 4, 3, 6 → \(2 \times 6 = 12 = 4 \times 3\). ✓
Hence, the answer is option B.
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Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
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:
