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प्रश्न
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
विकल्प
5, 10, 15, 20
4, 10, 16, 22
3, 7, 11, 15
none of these
उत्तर
5, 10, 15, 20
Let the four numbers in A.P. be as follows:
\[a - 2d, a - d, a, a + d\]
Their sum = 50 (Given)
\[\Rightarrow \left( a - 2d \right) + \left( a - d \right) + a + \left( a + d \right) = 50\]
\[ \Rightarrow 2a - d = 25 . . . . . \left( 1 \right)\]
\[\text { Also }, \left( a + d \right) = 4\left( a - 2d \right)\]
\[ \Rightarrow a + d = 4a - 8d\]
\[ \Rightarrow 3d = a . . . . . . \left( 2 \right)\]
From equations \[\left( 1 \right) \text { and }\left( 2 \right),\] , we get:
d = 5, a = 15
Hence, the numbers are
\[15 - 10, 15 - 5, 15, 15 + 5\], i.e. 5, 10, 15, 20.
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