Question
Download Solution PDF3 के चार क्रमागत गुणज का योग 78 है। इनमें से सबसे बड़ी संख्या है:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
3 के चार क्रमागत गुणज का योग = 78
गणना:
मान लीजिये कि 3 का पहला गुणज = 3a
इसी प्रकार, 3 का दूसरा गुणज = 3(a + 1)
⇒ 3 का तीसरा गुणज = 3(a + 2)
⇒ 3 का चौथा गुणज = 3(a + 3)
3a +3(a + 1) + 3(a + 2) + 3(a + 3) = 78
⇒ 3a + 3a + 3 + 3a + 6 + 3a + 9 = 78
⇒ 12a + 18 = 78
⇒ 12a = 78 - 18 = 60
⇒ a = 60/12 = 5
∴ 3 का सबसे बड़ा गुणज = 3(a + 3) = 3 × (5 + 3) = 24
Shortcut Trick गणना:
3 के क्रमागत 4 गुणजों का औसत = 78/4 = 19.5
तो, संख्या 18 और 21 होनी चाहिए।
तो श्रृंखला होगी
15, 18, 21, 24
∴ सबसे बड़ा गुणज 24 है।
Last updated on Jul 4, 2025
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