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When x is subtracted from each of 19, 28, 55 and 91. the numbers so obtained in this order are in proportion. What is the value
of x?
8
7
9
5
- Let’s call the four numbers after subtracting x:
(19–x), (28–x), (55–x), (91–x)
- These numbers are said to be in proportion, so:
(19–x)/(28–x) = (55–x)/(91–x)
- Cross-multiplied:
(19–x)(91–x) = (28–x)(55–x)
- Expand both sides:
19×91 – 19x – 91x + x² = 28×55 – 28x – 55x + x²
1729 – 110x + x² = 1540 – 83x + x²
- x² cancels:
1729 – 110x = 1540 – 83x
1729 – 1540 = 110x – 83x
189 = 27x
x = 7
- Now let’s check which option is correct:
- Option 1: 8
- Option 2: 7
- Option 3: 9
- Option 4: 5
- Correct answer is Option 2, 7.
By: santosh ProfileResourcesReport error
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