Synopsis IAS

Answer

Solution

UPSC Prelims

Mathematics

Theme:

LCM AND HCF / लघुत्तम समापवर्त्य एवं महत्तम समापवर्तक

Q6 2014, LCM AND HCF

Five persons fire bullets at a target at an interval of 6, 7, 8, 9 and 12 seconds respectively. The number of times they would fire the bullets together at the target in an hour is

पाँच व्यक्ति एक लक्ष्य पर क्रमशः 6, 7, 8, 9 और 12 सेकण्ड के अन्तराल पर गोलियाँ दागते हैं। एक घंटे में वे लक्ष्य पर एक साथ कितनी बार गोलियाँ दागेंगे ?

Explanation

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The five persons will together fire at the target at an interval of 'r second where

t = LCM (6, 7, 8, 9. 12)

LCM (6, 7, 8, 9, 12) = 2³x 3² x 7 = 504

⸫ t = 504 s

Number of seconds in an hour = 3600

⸫ Number of times the five persons would fire the bullets together at the target in an hour =

(where denotes the greatest integer less than or equal to t) = = 7

The five persons will together fire at the target at an
interval of 'r second where

t = LCM (6, 7, 8, 9. 12)

<v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
 <v:stroke join="">
 <v:formulas>
 <v:f eqn="if lineDrawn pixelLineWidth 0">
 <v:f eqn="sum @0 1 0">
 <v:f eqn="sum 0 0 @1">
 <v:f eqn="prod @2 1 2">
 <v:f eqn="prod @3 21600 pixelWidth">
 <v:f eqn="prod @3 21600 pixelHeight">
 <v:f eqn="sum @0 0 1">
 <v:f eqn="prod @6 1 2">
 <v:f eqn="prod @7 21600 pixelWidth">
 <v:f eqn="sum @8 21600 0">
 <v:f eqn="prod @7 21600 pixelHeight">
 <v:f eqn="sum @10 21600 0">
 </v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas>
 <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect">
 </v:path></v:stroke></v:shapetype><v:shape id="Picture_x0020_60" o:spid="_x0000_i1025" type="#_x0000_t75" alt="Description: Text

Description automatically generated with medium confidence">
 <v:imagedata src="file:///C:\Users\GAURAV~1\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png" o:title="Text

Description automatically generated with medium confidence">
</v:imagedata></v:shape>

LCM (6, 7, 8, 9, 12) = 23 x 32 x 7 =
504

⸫ t = 504 s

Number of seconds in an hour = 3600

⸫ Number of times the five persons would fire the bullets
together at the target in an hour = <v:shape id="_x0000_i1025" type="#_x0000_t75">
 <v:imagedata src="file:///C:\Users\GAURAV~1\AppData\Local\Temp\msohtmlclip1\01\clip_image002.png" o:title="" chromakey="white">
</v:imagedata></v:shape>

(where <v:shape id="_x0000_i1025" type="#_x0000_t75">
 <v:imagedata src="file:///C:\Users\GAURAV~1\AppData\Local\Temp\msohtmlclip1\01\clip_image003.png" o:title="" chromakey="white">
</v:imagedata></v:shape> denotes the greatest integer less than or
equal to t) = <v:shape id="_x0000_i1025" type="#_x0000_t75">
 <v:imagedata src="file:///C:\Users\GAURAV~1\AppData\Local\Temp\msohtmlclip1\01\clip_image004.png" o:title="" chromakey="white">
</v:imagedata></v:shape> = 7

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Q 6. 2014, LCM AND HCF

Mathematics

Explanation

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Mathematics

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Explanation

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