Question

1. find the number such that 8 is subtracted from 9 times the number,the result is more than twice the number.

2. Present age of A and B are in the ratio 5:6 two years ago , their ages were in the ratios 4:5. Find there present ages..

Answer 1

1. Let the number be x.
Given that, 9x - 8 = _ + 2x
The question is incomplete. It is not mentioned how much more than twice the number.

2. Let the present age of A and B be x and y respectively.
Given,
x/y = 5/6
6x = 5y
6x - 5y = 0 --- (i)

Two years ago their ages will be x-2 and y-2.
Given,
(x-2) / (y-2) = 4/5
5(x-2) = 4(y-2)
5x - 10 = 4y - 8
5x - 4y = 2 --- (ii)

(i)×5 ---> 30x - 25y = 0 --(1)
(ii)×6--> 30x - 24y =12 --(2)

(1)-(2) --> -y = -12
y = 12

(i) ---> x = 5y/6
x = (5×12)/6
x = 10

Present ages of A and B are 10 and 12 respectively.