Question

Three numbers are in the ratio 2:5:7.if 7 is subtracted from the second,the resulting number are in AP.find the numbers

Answer 1

GIVEN :–

• Three numbers are in the ratio 2 : 5 : 7.

• When 7 is subtracted from the second,the resulting number are in A.P.

SOLUTION :–

• Let the numbers are 2x , 5x , 7x .

• According to the question –

=> When 7 is subtracted from the second , the resulting number are in A.P.

• So that –

=> 2x , 5x - 7 , 7x are in A.P.

• Now Applying condition –

=> 2(5x - 7) = 2x + 7x

=> 10x - 14 = 9x

=> 10x - 9x = 14

=> x = 14

• Let the numbers => 2(14) , 5(14) , 7(14)

=> Numbers = 28 , 70 , 98

• Hence , The numbers are 28 , 70 , 98.

▪︎VERIFICATION :–

• Let's subtract '7' from second term –

=> 28 , 63 , 98 are in A.P.

=> 2(63) = 98 + 28

=> 126 = 126 ( Verified )

Answer 2

✯✯ QUESTION ✯✯

Three numbers are in the ratio 2:5:7....If 7 is subtracted from the second,the resulting number are in AP....Find the numbers.

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✰✰ ANSWER ✰✰

• Let the 1st No. be = 2x
• Let the 2nd No. be = 5x
• Let the 3rd No. be = 7x

➮As given that when 7 is subtracted from 2nd Term then No. are in A.P... So ,

$\implies\tt{2x(5x-7),7x}$

➥Now ,

$\implies\tt{2(5x-7)=2x+7x}$

$\implies\tt{10x-14=2x+7x}$

$\implies\tt{10x-14=9x}$

$\implies\tt{10x-9x=14}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{14}}}$

☛So , The value of x is 14..

_______________________

$\implies\tt{First\:Number=2(14)}$

$\implies\tt\bold{28}$

$\implies\tt{Second\:Number=5(14)}$

$\implies\tt\bold{70}$

$\implies\tt{Third\:Number=7(14)}$

$\implies\tt\bold{98}$

☛So , The numbers are 28,70 and 98...