Question

Let the sum of 3 numbers be 13680. If the first number is 3/5 of third number and the ratio between the second and the third numbers is 4:7, then firstb number is

Answer 1

Answer :-

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Given :-

• The sum of 3 numbers is 13680.

• The first number ( 1st ) is 3/5 of third number.

• the ratio between the second ( 2nd ) and the third ( 3rd ) numbers is 4:7

To find :-

• The first number.

Salutation :-

Let , the common ratio of 2nd and 3rd number be x.

Then , the 2nd and 3rd number be 4x and 7x.

Now , the 1st number will be = 3 / 5 × ( 7x ) = 21x / 5

Now , according to the question ,

1st number + 2nd number + 3rd number = 13680

=> 21x / 5 + 4x + 7x = 13680

=> ( 21x + 20x + 35x ) / 5 = 13680

=> ( 76x ) / 5 = 13680

=> x = 13680 × 5 / 76

=> x = 180 × 5

=> x = 900

•°• x = 900

Now , the 1st number be { 21x / 5 }

= ( 21 × 900 ) / 5

= 21 × 180

= 3780

•°• The first number be 3780.

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[ VERIFICATION ]

• The first number is = 3780

• The 2nd number is ( 4x ) = 4 × 900 = 3600

• The 3rd number is ( 7x ) = 7 × 900 = 6300

•°• L.H.S = 3780 + 3600 + 6300 = 13680

•°• R.H.S = 13680

•°• L.H.S = R.H.S [ • Proved ]

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