Question

Two numbers are in the ratio of 5:6 . If 7 is subtracted from each of the numbers, the ratio becomes 4:5 . Find the numbers.

Answer 1

Hint: As the two numbers are given as a ratio , you can find the values of those two numbers in terms of a single variable. After changing the numbers that are subtracting 7 from both the numbers you can write the new numbers in the form of the variable which is taken in first ratio. Now equate these into the ratio that is given after subtracting 7 from those numbers.

Complete step by step answer:
Let us suppose the given numbers are a , b
Given that the ratio of the numbers are 5 : 6
Which implies a : b = 5 : 6
Let us suppose a = 5x , b = 6x
Given that 7 is subtracted from each of the numbers ,
Let us take the changed number of a is c and the changed number of b is d
Which implies c = a – 7 which is equal to 5x – 7 and d = b – 7 which is equal to 6x – 7 ………( 1 )
Given that the ratio of the numbers after 7 is subtracted from each is 4 : 5
Which implies c : d = 4 : 5
=> ( c/d ) = ( 4/5 )
Substituting values of c and d in terms of x by equation ( 1 ) in the above equation we get ,
(5x – 7 / 6x – 7 ) = 4 / 5 ………..(2)
=> 25x – 35 = 24x – 28
=> x = 7

Then the number will be a = 5x = 35 and b = 6x = 42.

Note: While solving the equation (2) , make sure that the denominator is not zero, that is (6x-7) is not equal to 0 , x should not be ( 7/6) . Do not make calculation mistakes. Read the question properly. They have given to subtract 7 from both the numbers not a single number.