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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 number are together 21. The numbers are :
- a)(36, 42)
- b)(45, 36)
- c)(50, 41)
- d)(55, 46)
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Two numbers are such that twice the greaternumber exceeds twice the sm...
Given information:
- Twice the greater number exceeds twice the smaller number by 18
- 1/3 of the smaller number + 1/5 of the greater number = 21
To find:
- The two numbers
Solution:
Let the two numbers be x and y, where x is the smaller number and y is the greater number.
From the first statement, we can write:
2y = 2x + 18
Simplifying this equation, we get:
y - x = 9 ...(1)
From the second statement, we can write:
(1/3)x + (1/5)y = 21
Multiplying both sides by 15 to get rid of the fractions, we get:
5x + 3y = 315 ...(2)
Now we have two equations with two variables. We can solve for x and y by eliminating one of the variables.
Multiplying equation (1) by 3, we get:
3y - 3x = 27
Adding this equation to equation (2), we get:
5x + 3y - 3x + 27 = 315
Simplifying this equation, we get:
2x + 3y = 288
Multiplying equation (1) by 2, we get:
2y - 2x = 18
Adding this equation to equation (2), we get:
5x + 2y - 2x + 18 = 315
Simplifying this equation, we get:
3x + 2y = 297
Now we have two equations with two variables again. We can solve for x and y by eliminating one of the variables.
Multiplying the first equation by 2 and subtracting the second equation from it, we get:
(2x + 18) - (3x + 2y) = 18
Simplifying this equation, we get:
-x - 2y = -18
Multiplying equation (1) by -2 and adding it to this equation, we get:
-2y + 2x + 2y = -18 - 18
Simplifying this equation, we get:
x = 36
Substituting x = 36 in equation (1), we get:
y - 36 = 9
Simplifying this equation, we get:
y = 45
Therefore, the two numbers are 36 and 45.
Hence, the correct answer is option (B).
- Twice the greater number exceeds twice the smaller number by 18
- 1/3 of the smaller number + 1/5 of the greater number = 21
To find:
- The two numbers
Solution:
Let the two numbers be x and y, where x is the smaller number and y is the greater number.
From the first statement, we can write:
2y = 2x + 18
Simplifying this equation, we get:
y - x = 9 ...(1)
From the second statement, we can write:
(1/3)x + (1/5)y = 21
Multiplying both sides by 15 to get rid of the fractions, we get:
5x + 3y = 315 ...(2)
Now we have two equations with two variables. We can solve for x and y by eliminating one of the variables.
Multiplying equation (1) by 3, we get:
3y - 3x = 27
Adding this equation to equation (2), we get:
5x + 3y - 3x + 27 = 315
Simplifying this equation, we get:
2x + 3y = 288
Multiplying equation (1) by 2, we get:
2y - 2x = 18
Adding this equation to equation (2), we get:
5x + 2y - 2x + 18 = 315
Simplifying this equation, we get:
3x + 2y = 297
Now we have two equations with two variables again. We can solve for x and y by eliminating one of the variables.
Multiplying the first equation by 2 and subtracting the second equation from it, we get:
(2x + 18) - (3x + 2y) = 18
Simplifying this equation, we get:
-x - 2y = -18
Multiplying equation (1) by -2 and adding it to this equation, we get:
-2y + 2x + 2y = -18 - 18
Simplifying this equation, we get:
x = 36
Substituting x = 36 in equation (1), we get:
y - 36 = 9
Simplifying this equation, we get:
y = 45
Therefore, the two numbers are 36 and 45.
Hence, the correct answer is option (B).
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Community Answer
Two numbers are such that twice the greaternumber exceeds twice the sm...
2x - 2y=18=) x-y = 9=)equation 1
1/3 y +1/5 x =21 =) 5y +3x = 9*21=) 5y +3x = 315=)equation 2
Solving 1&2
5(x - y= 9) multiply by 5
3x +5y =315
5x - 5y =45
3x +5y =315
5x +3x = 45 +315
8x=360
x=45
Substitute in 1
45-y=9
45-9=y
36=y
Hence 45 & 36 is the answer
1/3 y +1/5 x =21 =) 5y +3x = 9*21=) 5y +3x = 315=)equation 2
Solving 1&2
5(x - y= 9) multiply by 5
3x +5y =315
5x - 5y =45
3x +5y =315
5x +3x = 45 +315
8x=360
x=45
Substitute in 1
45-y=9
45-9=y
36=y
Hence 45 & 36 is the answer
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Two numbers are such that twice the greaternumber exceeds twice the smallerone by 18 and 1/3 of the smaller and 1/5 of the greater number are together 21. The numbers are :a)(36, 42)b)(45, 36)c)(50, 41)d)(55, 46)Correct answer is option 'B'. Can you explain this answer?
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