Question

Two numbers are in the ratio of 6:11. If 6 is subtracted from each, the resulting numbers are in the ratio 4:9. The sum of the original numbers is

A) 44
B) 51
C) 62
D) 70

Answer 1

6x-6:11x-6=4:9

54x-54=44x-24

x=3

sum=6×3+11×3

=51

Answer 2

Sum of the original numbers is 51.

Step-by-step explanation:

Two numbers are in the ratio of 6 : 11.

Let the numbers be 6x and 11x.

If 6 is subtracted from each, the ratio becomes 4 : 9

$\frac{6x-6}{11x-6}=\frac{4}{9}$

Do cross multiplication.

9(6x - 6) = 4(11x - 6)

54x - 54 = 44x - 24

54x - 44x = 54 - 24

10x = 30

x = 3

The original numbers are:

6x = 6(3) = 18

11x = 11(3) = 33

Sum of the original numbers

              = 18 + 33

              = 51

Sum of the original numbers is 51.

To learn more...

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