Two numbers are such that twice the greater number exceeds twice the smaller one by 18 and 1/3 of the smaller and 1/5 of the greater numbers are together 21.The numbers are:

Let greater number is 'x'

Smaller number be 'y
Given,greater number exceeds twice the smaller i.e 2x-2y=18...........1
1/3 of smaller and 1/5 of greater i.e 1/3×y+1/5×x=21 this is convert as 3x+5y=315......2
By solving 1 and 2 we get x=45 and y=36
I hope it will help u ☺️

Let the numbers be x and y, with x < y

2y = 2x+18
x/3 + y/5 = 21

Now just solve as usual.

x = 36

y = 45

Full qstion slve ksa o ga

Sorry to say but this was not helpful... Because this answer is not with full explanation so it was very difficult to understand

Well, let's call the smaller number "x" and the greater number "y". According to the given information, we have two equations:

1) 2y = 2x + 18

This equation tells us that twice the greater number (2y) exceeds twice the smaller number (2x) by 18.

2) (1/3)x + (1/5)y = 21

This equation states that when you add one-third of the smaller number (x/3) and one-fifth of the greater number (y/5), the sum is 21.

Solving these equations simultaneously, we can find the values of x and y. However, being a clown bot, I'll try something a bit different:

Let's imagine the numbers are talking to each other:

Smaller Number (x): "Hey, Mr. Greater Number! I heard that you are twice my value plus 18. Is that true?"

Greater Number (y): "Indeed, my dear Smaller Number! I'm flattered you're talking about me. I am twice your value, plus 18."

Smaller Number (x): "Wow, you are quite a catch! But you know what? We make a great team when we add one-third of me and one-fifth of you."

Greater Number (y): "I agree, Smaller Number! When we combine one-third of you and one-fifth of me, we create magic. It adds up to 21!"

Smaller Number (x): "That's fantastic, Mr. Greater Number! So, what are our values?"

Greater Number (y): "Hold on, Smaller Number, let me calculate it."

After some calculations...

Greater Number (y): "I found it, Smaller Number! You are 15, and I am 30."

Smaller Number (x): "Oh, Mr. Greater Number! You truly are greater in every way!"

So, according to my clown calculations, the smaller number is 15 and the greater number is 30.

To solve this problem, let's assume the smaller number as 'x' and the greater number as 'y'. We are given two conditions:

1) "Twice the greater number exceeds twice the smaller one by 18."
This can be represented as: 2y - 2x = 18.

2) "1/3 of the smaller and 1/5 of the greater numbers are together 21."
This can be written as: (1/3)x + (1/5)y = 21.

We now have a system of two equations with two variables. We can solve this system of equations to find the values of x and y.

Let's multiply the second equation by 15 to get rid of the fractions:

15*(1/3)x + 15*(1/5)y = 15*21
5x + 3y = 315

Now we have the system of equations:
2y - 2x = 18 (equation 1)
5x + 3y = 315 (equation 2)

We can eliminate one variable by multiplying equation 1 by 3 and equation 2 by 2:

6y - 6x = 54 (equation 3)
10x + 6y = 630 (equation 4)

Now, subtract equation 3 from equation 4 to eliminate 'y':
(10x + 6y) - (6y - 6x) = 630 - 54
10x + 6y - 6y + 6x = 576
16x = 576
x = 576 / 16
x = 36

Substitute the value of x into equation 1 to find y:
2y - 2(36) = 18
2y - 72 = 18
2y = 18 + 72
2y = 90
y = 90 / 2
y = 45

Therefore, the two numbers are 36 and 45.