Question

4. Two numbers are such that the ratio between
them is 3:5. If each is increased by 10, the ratio
between the new numbers so formed is 5:7. Find
the original numbers.​

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assume

The two numbers be p and n

${\boxed{\sf\:{1^{st} \;Situation}}}$

p : n = 3 : 5

5p = 3n

$\tt{\rightarrow p=\dfrac{3n}{5}....(1)}$

Hence

${\boxed{\sf\:{2^{nd} \;Situation}}}$

(p + 10) : (n + 10) = 5 : 7

7(p + 10) = (n + 10)5

7p + 70 = 5n + 50

7p + 70 - 50 = 5n

7p + 20 = 5n ........... (2)

${\boxed{\sf\:{Put\;value\;of\;p\; from\;(1)}}}$

$\tt{\rightarrow 7\times\dfrac{3n}{5}+20=5n}$

$\tt{\rightarrow\dfrac{21n+100}{5}=5n}$

21n + 100 = 25n

100 = 25n - 21n

100 = 4n

$\tt{\rightarrow\dfrac{100}{4}=n}$

25 = n

Hence,

n = 25

${\boxed{\sf\:{Put\;value\;of\;n\;in\;(1)}}}$

$\tt{\rightarrow p=3\times\dfrac{25}{5}}$

p = 3 × 5

p = 15

$\Large{\boxed{\sf\:{Original\;Numbers}}}$

= 15 and 25

Answer 2

Answer:

15 and 25 are the original numbers.

Step-by-step explanation:

Let the numbers be 3x and 5x.

Acc to question

3x+10=5x and 5x+10=7x

5x-3x=10

2x=10

x=5

Original Numbers-

3x=5*3=15

5x=5*5=25

Verify-

3x+10=5x

15+10=5x

25=25

Hence Verified

Hope it helps

It is the correct answer only ..it is another method to find the answer ...check it correctly before deleting it