# When 5 is subtracted from the greater number and 7 is subtracted from the smaller number, then the ratio of numbers becomes 3 ‚ą∂ 1. What is the value o

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When 5 is subtracted¬†from¬†the greater number and 7 is subtracted from the smaller number, then the ratio of numbers becomes 3 ‚ą∂¬†1. What is the value of the greater¬†number if the sum of numbers is 24?

1. 16
2. 14
3. 10
4. 12

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Correct Answer - Option 2 : 14

Given:

After subtracting¬†5 from¬†the greatest number and 7 from the smallest number, then the ratio is 3¬†‚ą∂ 1¬†

Also, the sum of the numbers is 24

Concept Used:

A ratio indicates how many times one number contains another.

Calculation:

Let the numbers be x and y¬†respectively

‚ąī x + y = 24¬† ¬† ¬† ----(1)

Also, when subtraction¬†of 5 from¬†the greatest number and subtraction of 7 from the smallest number, then the ratio is 3¬†‚ą∂ 1

So,¬†¬†${x - 5 \ \over y - 7} ={3 \ \over 1}$

‚áí 1 √ó (x -¬†5) = 3¬†√ó (y - 7)

‚áí x -¬†5¬†= 3y¬†- 21

‚áí x - 3y = -16¬† ¬† ¬† (2)

Solving equation (1) and (2), we get

x = 14 and y = 10

The greater¬†number = 14

‚ąī The greater¬†number is 14.