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The sum of four numbers is 253. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?
- a)72
- b)132
- c)60
- d)66
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The sum of four numbers is 253. The ratio of the first number to the s...
Let the 1stno. A = X
2nd no.= B , 3rd no.= C , 4th no. = D
A: B =2:3
A/B = 2/3
x/B =2/3
B= 3x/2
B:C=5:6
(3x/2)/ C= 5/6
C=( 6×3x)/2×5= 9x/5
C= 9x/5
C:D= 8:9
9x/5/ D = 8/9
D= (9x×9)/8×5= 81x/40
D= 81x/40
A+B+C+D= 253. (GIVEN)
x+ 3x/2+9x/5+81x/40
Lcm = 40
(40x+ 60x+ 72x+81x)/40= 253
253x= 253×40
X= (253×40)/253= 40
Ist no.(A)= X= 40
2no.(B)= 3x/2=( 3 × 40)/2= 60
3rd no.(C)= 9x/5 = (9×40)/5= 72
4th no.(D)= 81x/40=( 81×40/)/40= 81
Average of numbers= sum of observations/ total no.of observations
Average of 2nd no. & 3rd no.= (60+72)/2= 132/2= 66
2nd no.= B , 3rd no.= C , 4th no. = D
A: B =2:3
A/B = 2/3
x/B =2/3
B= 3x/2
B:C=5:6
(3x/2)/ C= 5/6
C=( 6×3x)/2×5= 9x/5
C= 9x/5
C:D= 8:9
9x/5/ D = 8/9
D= (9x×9)/8×5= 81x/40
D= 81x/40
A+B+C+D= 253. (GIVEN)
x+ 3x/2+9x/5+81x/40
Lcm = 40
(40x+ 60x+ 72x+81x)/40= 253
253x= 253×40
X= (253×40)/253= 40
Ist no.(A)= X= 40
2no.(B)= 3x/2=( 3 × 40)/2= 60
3rd no.(C)= 9x/5 = (9×40)/5= 72
4th no.(D)= 81x/40=( 81×40/)/40= 81
Average of numbers= sum of observations/ total no.of observations
Average of 2nd no. & 3rd no.= (60+72)/2= 132/2= 66
Most Upvoted Answer
The sum of four numbers is 253. The ratio of the first number to the s...
Given information:
- Sum of four numbers = 253
- Ratio of first number to second number = 2:3
- Ratio of second number to third number = 5:6
- Ratio of third number to fourth number = 8:9
Let's assume the four numbers as 2x, 3x, 5y, and 6y (where x and y are constants).
Using the given ratios, we can write:
- (2x + 3x + 5y + 6y) = 253 (sum of four numbers)
- 2x/3x = 2/3 (ratio of first number to second number)
- 3x/5y = 3/5 (ratio of second number to third number)
- 5y/6y = 5/6 (ratio of third number to fourth number)
Simplifying these equations, we get:
- 10x + 11y = 253
- x = (3/2)y
- x = (9/5)y
- y = 45
Therefore, the four numbers are: 30, 45, 225, and 270
The average of the second number and the third number = (45 + 225)/2 = 135
Hence, the correct answer is option D (66).
- Sum of four numbers = 253
- Ratio of first number to second number = 2:3
- Ratio of second number to third number = 5:6
- Ratio of third number to fourth number = 8:9
Let's assume the four numbers as 2x, 3x, 5y, and 6y (where x and y are constants).
Using the given ratios, we can write:
- (2x + 3x + 5y + 6y) = 253 (sum of four numbers)
- 2x/3x = 2/3 (ratio of first number to second number)
- 3x/5y = 3/5 (ratio of second number to third number)
- 5y/6y = 5/6 (ratio of third number to fourth number)
Simplifying these equations, we get:
- 10x + 11y = 253
- x = (3/2)y
- x = (9/5)y
- y = 45
Therefore, the four numbers are: 30, 45, 225, and 270
The average of the second number and the third number = (45 + 225)/2 = 135
Hence, the correct answer is option D (66).
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Community Answer
The sum of four numbers is 253. The ratio of the first number to the s...
► Let the 1stno. = A = x
2nd no.= B , 3rd no.= C , 4th no. = D
► A:B = 2:3
A/B = 2/3
x/B = 2/3
B = 3x/2
► B:C = 5:6
(3x/2)/C = 5/6
C = (6*3x)/2*5 = 9x/5
C = 9x/5
► C:D = 8:9
9x/5/D = 8/9
D = (9x*9)/8*5 = 81x/40
D = 81x/40
► A + B + C + D = 253. (Given)
⇒ x + 3x/2 + 9x/5 + 81x/40 = 253
⇒ (40x+ 60x+ 72x+81x)/40 = 253
⇒ 253x = 253*40
⇒ X = (253*40)/253 = 40
⇒ 1st no.(A) = X = 40
⇒ 2nd no.(B) = 3x/2 =( 3 × 40)/2 = 60
⇒ 3rd no.(C) = 9x/5 = (9×40)/5 = 72
⇒ 4th no.(D) = 81x/40 =( 81×40/)/40 = 81
► Average of numbers = sum of observations/ total no.of observations
► Average of 2nd no. & 3rd no.= (60+72)/2 = 132/2 = 66
2nd no.= B , 3rd no.= C , 4th no. = D
► A:B = 2:3
A/B = 2/3
x/B = 2/3
B = 3x/2
► B:C = 5:6
(3x/2)/C = 5/6
C = (6*3x)/2*5 = 9x/5
C = 9x/5
► C:D = 8:9
9x/5/D = 8/9
D = (9x*9)/8*5 = 81x/40
D = 81x/40
► A + B + C + D = 253. (Given)
⇒ x + 3x/2 + 9x/5 + 81x/40 = 253
⇒ (40x+ 60x+ 72x+81x)/40 = 253
⇒ 253x = 253*40
⇒ X = (253*40)/253 = 40
⇒ 1st no.(A) = X = 40
⇒ 2nd no.(B) = 3x/2 =( 3 × 40)/2 = 60
⇒ 3rd no.(C) = 9x/5 = (9×40)/5 = 72
⇒ 4th no.(D) = 81x/40 =( 81×40/)/40 = 81
► Average of numbers = sum of observations/ total no.of observations
► Average of 2nd no. & 3rd no.= (60+72)/2 = 132/2 = 66
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The sum of four numbers is 253. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?a)72b)132c)60d)66Correct answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The sum of four numbers is 253. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?a)72b)132c)60d)66Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of four numbers is 253. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?a)72b)132c)60d)66Correct answer is option 'D'. Can you explain this answer?.
The sum of four numbers is 253. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?a)72b)132c)60d)66Correct answer is option 'D'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The sum of four numbers is 253. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?a)72b)132c)60d)66Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of four numbers is 253. The ratio of the first number to the second number is 2:3. The ratio of the second number to the third number is 5:6. The ratio of the third number to the fourth number is 8:9. What is the average of the second number and the third number?a)72b)132c)60d)66Correct answer is option 'D'. Can you explain this answer?.
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