When k is subtracted from each of 23, 35, 55 and 91, the numbers so obtained in this order are in proportion. What is the value of k?Options :9783

The problem is asking for a value of 'k' such that when 'k' is subtracted from each of the numbers 23, 35, 55, and 91, the resulting numbers form a proportion.

A proportion is an equation stating that two ratios are equal. If the numbers a, b, c, and d (in that order) form a proportion, then the ratio of a to b is equal to the ratio of c to d.

So, we can set up the following equation to solve for 'k':

(23 - k) / (35 - k) = (55 - k) / (91 - k)

Cross-multiplying gives us:

(23 - k) * (91 - k) = (35 - k) * (55 - k)

Expanding both sides gives us:

2103 - 114k + k^2 = 1925 - 90k + k^2

Simplifying gives us:

178 = 24k

Finally, solving for 'k' gives us:

k = 178 / 24 = 7.41666667

So, the value of 'k' that makes the numbers 23, 35, 55, and 91 form a proportion when 'k' is subtracted from each is approximately 7.42.