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Question

If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are



A

5, 10, 15, 20

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B

4, 10, 16, 22

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C

3, 7, 11, 15

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D

None of these

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Solution

The correct option is C

5, 10, 15, 20


Let the four numbers in A.P. be as follows:

a - 2d, a - d, a + d

Their sum = 50 (Given)

(a2d)+(ad)a+(a+d)=50

2ad=25

Also, (a+d)=4(a2d)

a+d=4a8d

3d=a

From equations (1) and (2), we get:

d = 5, a = 15

Hence, the numbers are 15 - 10, 15 - 5, 15, 15 + 5, i.e., 5, 10, 15, 20.


Mathematics
RD Sharma
Standard XI

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