Question

14. Find two numbers in the ratio of 5 to 5 such that when each is
diminished by 12, they shall become in the ratio of 3 to 3.​

Answer 1

Answer:

Let,

two no. is x:y in ratio 40/7:5

x:y = 40/7:5

x = 40/35y

x = 8/7 y

when each is diminished by 25/2 ,they shall become in the ratio 11/3 to 3

x-25/2:y-25/2= 11/3:3

2x-25/2:2y-25/2=11/3:3

3(2x-25/2)=11/3(2y-25/2)

6x-75 = 22y-275/3

18x-225=22y-275

18x-22y=-50

on putting the value of x in eqn

18(8/7y)-22y=-50

144y-154y=-350

-10y=-350

y=35

on putting the value of y in x

x= 8/7×35

x= 8×5

x= 40

Therefore, the nos are 35 and 40

Answer 2

Answer:

(5 + 5/7) / 5 = (1 + 1/7) / 1 = 8/7

(3 + 2/3) / 3 = 1 + 2/9 = 11/9

(8x - (12 + 1/2)) / (7x - (12 + 1/2)) = 11 / 9

9 * (8x - 12 - 1/2) = 11 * (7x - 12 - 1/2)

72x - 108 - 9/2 = 77x - 132 - 11/2

132 - 108 + 11/2 - 9/2 =77x - 72x

24 + 2/2 = 5x

24 + 1 = 5x

25 = 5x

5 = x

8x = 8 * 5 = 40

7x = 7 * 5 = 35

40,35