The sum of three numbers is 124. If the ratio | vedclass

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(A) Let the three numbers be $A, B,$ and $C$.We are given the ratios $A:B = 2:3$ and $B:C = 7:9$.To find the combined ratio $A:B:C$,we equate the valu

Vedclass · Accepted Answer

$54$

Vedclass · Answer

(A) Let the three numbers be $A, B,$ and $C$.We are given the ratios $A:B = 2:3$ and $B:C = 7:9$.To find the combined ratio $A:B:C$,we equate the value of $B$ in both ratios.The least common multiple of $3$ and $7$ is $21$.Multiplying the first ratio by $7$ and the second ratio by $3$,we get:$A:B = (2 	imes 7) : (3 	imes 7) = 14:21$$B:C = (7 	imes 3) : (9 	imes 3) = 21:27$Thus,$A:B:C = 14:21:27$.Let the numbers be $14x, 21x,$ and $27x$.The sum of the numbers is $124$,so $14x + 21x + 27x = 124$.$62x = 124$,which gives $x = 2$.The third number is $27x = 27 	imes 2 = 54$.

The sum of three numbers is $124$. If the ratio between the first and second is $2:3$ and that between the second and third is $7:9$,then the third number is

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