Question

The ratio of two numbers is 6:11. if their difference is 35, what is the smallest number? ​

Answer 1

The smallest number is 42

Explanation:

Let the numbers be x and y

their ratio is 6:11

so,

x:y = 6:11

or,

x/y = 6/11

11x = 6y (i)

and their difference is 35 so,

if y is the bigger number,

y - x = 35 (ii)

so we have system of equations,

11x = 6y (i)

y - x = 35 (ii)

Solving this for x and y,

using (i), we get,

y = 11x/6

putting this into (ii),

(11/6)x - x = 35

(11x - 6x)/6 = 35

(5/6)x = 35

x = (6/5)(35)

x = (6)(7)

x = 42

And since y = 11x/6,

y = (11)(42/6)

y = 77

Hence the smallest number is 42