Question

the 3 numbers a,b,c in the ratio of a:b=3:4 and b:c=5:6 have a sum of 118.what are the values of a,b,c​

Answer 1

$Given \: a : b = 3: 4$

/* Multiplying numerator and denominator by 5 , we get */

$\implies a:b = 15 : 20\: --(1)$

$Given \:b : c = 5:6$

/* Multiplying numerator and denominator by 4, we get */

$\implies b:c = 20 : 24\: --(2)$

/* From (1) and (2) , we get */

$a : b : c = 15 : 20 : 24 \: --(3)$

$Let a = 15x , b = 20x \: and\: c = 24x$

$Sum \: of \: the: numbers = 118 \: (given)$

$\implies 15x + 20x + 24x = 118$

$\implies 59x = 118$

$\implies x = \frac{118}{59}$

$\implies x = 2$

Therefore.,

$a = 15x = 15 \times 2 = 30$

$b = 20x = 20 \times 2 = 40$

$c = 24x = 24 \times 2 = 48$

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