1.

If (a : b) = 3 : 5, then find the value of (3a + 4b) : (5a + 3b).1). 31 : 322). 29 : 303). 27 : 314). 29 : 31

Answer»

Let a = 3x and b = 5x, then according to the question,

(3a + 4b) : (5A + 3b) = (3a + 4b)/(5a + 3b)

⇒ (3a + 4b) : (5a + 3b) = (9x + 20x)/(15x + 15x) = 29x/30x = 29/30

⇒ (3a + 4b) : (5a + 3b) = 29 : 30

Hence, the required ratio is 29 : 30.

Alternate Method:

(3a + 4b) : (5a + 3b)

$(= \frac{{3\frac{a}{b} + 4}}{{5\frac{a}{b} + 3}} = \frac{{3 \times \frac{3}{5} + 4}}{{5 \times \frac{3}{5} + 3}} = \frac{{\LEFT( {9 + 20} \right) \times \frac{1}{5}}}{{3 + 3}})$

= 29/(6× 5) = 29/30 = 29 : 30

Hence, the required ratio is 29 : 30.



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