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

Given, when one is added to two numbers, their ratio becomes

3 : 4

.
When

5

is subtracted from the numbers, the ratio becomes

7 : 10

.
Let the two numbers be

x

and

y

.
According to the given condition,
⇒

\frac{x + 1}{y + 1} = \frac{3}{4}

⇒

4 x + 4 = 3 y + 3

⇒

4 x - 3 y = - 1

........

(1)

Also,

\frac{x - 5}{y - 5} = \frac{7}{10}

.
⇒

10 x - 50 = 7 y - 35

⇒

10 x - 7 y = 15

.......

(2)

Multiply equations

(1)

and

(2)

7

and

3

respectively.

28 x - 21 y = - 7 \dots . (3)

30 x - 21 y = 45

......

(4)

Subtracting

(3)

from

(4)

,
⇒

2 x = 52

\Rightarrow x = 26

Putting the value of

x

in (1)
⇒

4 (26) - 3 y = - 1

⇒

- 3 y = - 105

⇒

y = 35

∴

Numbers are

26, 35

.
Hence, the correct option is 3.

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