Question

24. Two numbers are i added to
number, the ratio becomes 7: 8. Find the numbers.
(Ans. 10 and 14]
5 If 10 be added to each number​

Answer 1

Answer:

Step-by-step explanation:

When 1 is added to each of the given two numbers, their ratio becomes 3:4 and when 5 is subtracted from each, the ratio becomes 7:10. What are the numbers?

Call the numbers a and b , we know:

a+1b+1=34

a−5b−5=710

Transforming 2. to a :

a−5b−5=710∣10(b−5)

10(a−5)=7(b−5)∣ extend

10a−50=7b−35∣+50

10a=7b+15∣÷10

a=7b10+32

Putting into 1.:

a+1b+1=34∣a=7b10+32

(7b10+32)+1b+1=34∣32+1=52

7b10+52b+1=34∣7b10+52=7b+2510

7b+2510b+1=34∣b+1=b+11

7b+2510b+11=34∣αβγδ=αβ×δγ=αδβγ

7b+2510(b+1)=34∣×40(b+1)

4(7b+25)=30(b+1)∣ extend

28b+100=30b+30∣−28b−30,⟺

2b=70∣÷2

b=35

a=7⋅3510+32=24510+32=492+32=49+32=522=26

The numbers are 26 and 35 .