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The sum of 40 A.M.’s between two number is 120. The sum of 50 A.M.’s between them is equal to
- a)150
- b)130
- c)160
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The sum of 40 A.M.’s between two number is 120. The sum of 50 A....
Let A1, A2, A3, , A40 be 40 A.M's between two numbers 'a' and 'b'.
Then,
a, A1, A2, A3, , A40, b is an A.P. with common difference d = (b - a)/(n + 1) = (b - a)/41
[ where n = 40]
now,
A1, A2, A3, , A40 = 40/2( A1 + A40)
A1, A2, A3, , A40 = 40/2(a + b)
[ a, A1, A2, A3, , A40, b is an Ap then ,a + b = A1 + A40]
sum of 40A.M = 120(given)
120= 20(a + b)
=> 6 = a + b --(1)
Again ,
consider B1, B2, B50 be 50 A.M.'s between two numbers a and b.
Then, a, B1, B2,, B50, b will be in A.P. with common difference = ( b - a)/51
now , similarly,
B1, B2, ... , B50 = 50/2(B1 + B2)
= 25(6) -from(1)
= 150
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Community Answer
The sum of 40 A.M.’s between two number is 120. The sum of 50 A....
The given question is related to arithmetic means (A.M.). We are given two numbers and we need to find the sum of a certain number of arithmetic means between them.
Let's assume the two numbers are a and b, where a < b.="" we="" are="" given="" that="" the="" sum="" of="" 40="" a.m.s="" between="" a="" and="" b="" is="" 120.="" />
To find the sum of 40 A.M.s between a and b, we can use the formula:
Sum = (Number of A.M.s / 2) * (First A.M. + Last A.M.)
Substituting the given values, we have:
120 = (40/2) * (First A.M. + Last A.M.)
Simplifying, we get:
120 = 20 * (First A.M. + Last A.M.)
Dividing both sides by 20, we obtain:
6 = First A.M. + Last A.M. ...............(1)
Next, we are given that the sum of 50 A.M.s between a and b is equal to some value. Let's assume this value is S. We can use the same formula to find the sum of 50 A.M.s:
S = (50/2) * (First A.M. + Last A.M.)
Simplifying, we have:
S = 25 * (First A.M. + Last A.M.)
Now, we need to determine the value of S.
Since the sum of 40 A.M.s is 120, we know that the sum of the additional 10 A.M.s must be 0. This is because if the sum of the additional 10 A.M.s was any other value, the sum of the 50 A.M.s would not be equal to 120.
Therefore, by adding 0 to the sum of the 40 A.M.s, we have:
S = 120 + 0 = 120
Hence, the sum of 50 A.M.s between the two numbers is 120.
But the question asks for the value of S in terms of a, b, and the two numbers of A.M.s. This means that we need to express S in terms of a and b.
From equation (1), we know:
6 = First A.M. + Last A.M.
Rearranging, we have:
First A.M. = 6 - Last A.M.
Substituting this into the equation for S, we get:
S = 25 * ((6 - Last A.M.) + Last A.M.)
Simplifying, we obtain:
S = 25 * 6 = 150
Hence, the sum of 50 A.M.s between the two numbers is 150.
Therefore, the correct answer is option A) 150.
Let's assume the two numbers are a and b, where a < b.="" we="" are="" given="" that="" the="" sum="" of="" 40="" a.m.s="" between="" a="" and="" b="" is="" 120.="" />
To find the sum of 40 A.M.s between a and b, we can use the formula:
Sum = (Number of A.M.s / 2) * (First A.M. + Last A.M.)
Substituting the given values, we have:
120 = (40/2) * (First A.M. + Last A.M.)
Simplifying, we get:
120 = 20 * (First A.M. + Last A.M.)
Dividing both sides by 20, we obtain:
6 = First A.M. + Last A.M. ...............(1)
Next, we are given that the sum of 50 A.M.s between a and b is equal to some value. Let's assume this value is S. We can use the same formula to find the sum of 50 A.M.s:
S = (50/2) * (First A.M. + Last A.M.)
Simplifying, we have:
S = 25 * (First A.M. + Last A.M.)
Now, we need to determine the value of S.
Since the sum of 40 A.M.s is 120, we know that the sum of the additional 10 A.M.s must be 0. This is because if the sum of the additional 10 A.M.s was any other value, the sum of the 50 A.M.s would not be equal to 120.
Therefore, by adding 0 to the sum of the 40 A.M.s, we have:
S = 120 + 0 = 120
Hence, the sum of 50 A.M.s between the two numbers is 120.
But the question asks for the value of S in terms of a, b, and the two numbers of A.M.s. This means that we need to express S in terms of a and b.
From equation (1), we know:
6 = First A.M. + Last A.M.
Rearranging, we have:
First A.M. = 6 - Last A.M.
Substituting this into the equation for S, we get:
S = 25 * ((6 - Last A.M.) + Last A.M.)
Simplifying, we obtain:
S = 25 * 6 = 150
Hence, the sum of 50 A.M.s between the two numbers is 150.
Therefore, the correct answer is option A) 150.
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The sum of 40 A.M.’s between two number is 120. The sum of 50 A.M.’s between them is equal toa)150b)130c)160d)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The sum of 40 A.M.’s between two number is 120. The sum of 50 A.M.’s between them is equal toa)150b)130c)160d)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of 40 A.M.’s between two number is 120. The sum of 50 A.M.’s between them is equal toa)150b)130c)160d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
The sum of 40 A.M.’s between two number is 120. The sum of 50 A.M.’s between them is equal toa)150b)130c)160d)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The sum of 40 A.M.’s between two number is 120. The sum of 50 A.M.’s between them is equal toa)150b)130c)160d)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of 40 A.M.’s between two number is 120. The sum of 50 A.M.’s between them is equal toa)150b)130c)160d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
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