Question

the three numbers are in the ratio of 3:7:9.if 5 is subtracted from the 2nd .the resulting no.form an a.p..find number

Answer 1

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ANS :

.............. 15 , 30 , 45 , ...............

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GIVEN :

=> THREE NO. ARE IN THE RATIO :

=> 3 : 7 : 9

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LET,

=> X BE THE COMMON MULTIPLE OF THIS RATIO

SO,

1ST NO. :

=> 3X

2ND NO.

=> 7X

3RD NO.

=> 9X

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ACCORDING TO GIVEN CONDITION :

=> IF 5 IS SUBSTRACTED FROM 2ND TERM THE TERMS WILL BE IN AP

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SECOND TERM :

=> 7X

NEW TERM :

=> 7X - 5

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=> 3X , ( 7X - 5 ) , 9X ARE IN AP

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KEY FORMULA :

$d \: = \: common \: difference \: between \: two \: consecutive \: terms$

SO,

=> ( 7X - 5 ) - 3X = 9X - ( 7X - 5 )

=> 4X - 5 = 2X + 5

=> 4X - 2X = 5 + 5

=> 2X = 10

=> X = 10 / 2

=> X = 5

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AP :

=> 3X , ( 7X - 5 ) , 9X

=> 3 * 5 , ( 7 * 5 - 5 ) , 9 * 5

=> 15 , 35 - 5 , 45

=> 15 , 30 , 45

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