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The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and that of the second to the third is 5:8, then the second number is :
- a)20
- b)30
- c)48
- d)58
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The sum of three numbers is 98. If the ratio of the first to the secon...
Let the 3 numbers be a, b and c
a : b = 2 : 3
b : c = 5 : 8
__________
⇒ a : b : c = 10 : 15 : 24
Hence,
10x + 15x + 24x = 98
⇒ 49x = 98
⇒ x = 2
⇒ 2nd number is 15x ie 30
View all questions of this test
a : b = 2 : 3
b : c = 5 : 8
__________
⇒ a : b : c = 10 : 15 : 24
Hence,
10x + 15x + 24x = 98
⇒ 49x = 98
⇒ x = 2
⇒ 2nd number is 15x ie 30
Most Upvoted Answer
The sum of three numbers is 98. If the ratio of the first to the secon...
To solve this problem, we need to set up a system of equations using the given information and then solve for the second number.
Let's assume the three numbers are x, y, and z.
According to the given information:
1. The sum of the three numbers is 98.
x + y + z = 98
2. The ratio of the first number to the second number is 2:3.
x/y = 2/3
3. The ratio of the second number to the third number is 5:8.
y/z = 5/8
Now, let's solve these equations step by step.
Solving the first equation:
x + y + z = 98
Solving the second equation:
x/y = 2/3
Cross multiplying, we get:
3x = 2y
x = (2/3)y
Solving the third equation:
y/z = 5/8
Cross multiplying, we get:
8y = 5z
z = (8/5)y
Substituting the values of x and z in terms of y into the first equation:
(2/3)y + y + (8/5)y = 98
(10/15)y + (15/15)y + (24/15)y = 98
(49/15)y = 98
49y = 98*15
49y = 1470
y = 1470/49
y = 30
Therefore, the second number is 30.
Hence, the correct answer is option B.
Let's assume the three numbers are x, y, and z.
According to the given information:
1. The sum of the three numbers is 98.
x + y + z = 98
2. The ratio of the first number to the second number is 2:3.
x/y = 2/3
3. The ratio of the second number to the third number is 5:8.
y/z = 5/8
Now, let's solve these equations step by step.
Solving the first equation:
x + y + z = 98
Solving the second equation:
x/y = 2/3
Cross multiplying, we get:
3x = 2y
x = (2/3)y
Solving the third equation:
y/z = 5/8
Cross multiplying, we get:
8y = 5z
z = (8/5)y
Substituting the values of x and z in terms of y into the first equation:
(2/3)y + y + (8/5)y = 98
(10/15)y + (15/15)y + (24/15)y = 98
(49/15)y = 98
49y = 98*15
49y = 1470
y = 1470/49
y = 30
Therefore, the second number is 30.
Hence, the correct answer is option B.
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The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and that of the second to the third is 5:8, then the second number is :a) 20 b) 30 c) 48 d) 58 Correct answer is option 'B'. Can you explain this answer?
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