Question

find the two numbers such that 1/3 of the first number added to 1/5 of the second number gives 20 .1/6 of the first numbers added to 1/12th of the second gives nine. find the numbers

Answer 1

Answer :

Let us take the two numbers as x and y

Then,

x/3 + y/5 = 20

⇒ (5x + 3y)/15 = 20

⇒ 5x + 3y = 300 ...(i)

and

x/6 + y/12 = 9

⇒ (2x + y)/12 = 9

⇒ 2x + y = 108

⇒ 6x + 3y = 324 ...(ii),
multiplying both sides by 3

Now, (ii) - (i) ⇒

6x - 5x = 324 - 300

⇒ x = 24

Putting x = 24 in (i), we get

5 (24) + 3y = 300

⇒ 120 + 3y = 300

⇒ 3y = 300 - 120

⇒ 3y = 180

⇒ y = 60

∴ the two numbers are 24 and 60

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