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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:

a2d,ad,a,a+d

Their sum = 50 (Given)

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

2ad=25(i)

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

a+d=4a8d

3d=a(ii)

From equations (i) and (ii), we get

d=5,a=15

Hence, the numbers are 1510,155,15,15+5, i.e., 5,10,15,20.


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