question_answer

Two numbers are in the ratio 5 : 7. On diminishing each of them by 40, they become in the ratio 17 : 27. The difference of the numbers is

A)  18                               

B)  52

C)  175                             

D)  50

Correct Answer: D

Solution :

Let the two numbers are x and y.                   According to the question.                        \[\frac{x}{y}=\frac{5}{7}7x=5y\] \[7x-5y=0\]                                ...(i) Again,   \[\frac{x-40}{y-40}=\frac{17}{27}\] \[\Rightarrow \]   \[27x-1080=17y-680\] \[\Rightarrow \]   \[27x-17y=1080-680\] \[\Rightarrow \]   \[27x-17y=400\]             ?(ii) From Eq. (i) \[x\,\,17-\]Eq. (ii)\[x,5\] we get \[\therefore \]                  \[x=125\] Putting the value of x in Eq. (i), we get \[7\times 125=5y\]             \[\therefore \]      \[\frac{7\times 125}{5}=175\] \[\therefore \]Difference of the numbers\[=175-125=50\]