Question

Which of the following ratios is the largest?
A. \[7:15\]
B. \[15:23\]
C. \[17:25\]
D. \[21:29\]

Answer 1

Hint: We are asked which of the given ratios is the largest. For this you will need to recall the concept of ratios. Use those concepts to find the value of the given ratios one by one. Then compare the values obtained for each ratio and select the one with the largest value.

Complete step-by-step answer:
Whenever ratio of two numbers are given we can write it as,
 \[x:y = \dfrac{x}{y}\]
To find out which of the given ratio is the largest, we check the given ratios one by one by finding the values of each ratio
Option (A) \[7:15\]
 \[7:15\] can be written as,
 \[7:15 = \dfrac{7}{{15}}\]
 \[ \Rightarrow 7:15 = 0.46\] -------(i)

Option (B) \[15:23\]
 \[15:23\] can be written as,
 \[ \Rightarrow 15:23 = 0.65\] --------(ii)

Option (C) \[17:25\]
 \[17:25\] can be written as,
 \[17:25 = \dfrac{{17}}{{25}}\]
 \[ \Rightarrow 17:25 = 0.68\] ------(iii)

Option (D) \[21:29\]
 \[21:29\] can be written as,
 \[21:29 = \dfrac{{21}}{{29}}\]
 \[ \Rightarrow 21:29 = 0.72\] ---------(iv)
Now, comparing the equations (i), (ii), (iii) and (iv) we observe that the value of \[21:29\] is the largest. Therefore the ratio \[21:29\] is the largest.
Hence, the correct answer is option (D) \[21:29\] .
So, the correct answer is “Option D”.

Note: Ratio determines the relation between two numbers or how many times a number is within the other number. One more alternative to find the largest ratio is that making the denominator equal for all the ratios. To make the denominator equal for all the ratios we need to find the L.C.M of denominators of all the ratios. After we make the denominators equal then we can easily compare the ratios, we can observe the difference between the numerator and denominator and the ratio having the least difference between the denominator and numerator will give us the largest value.