If a-3-b-7- 4a - 5b-Q- Find the value of Q-

Given nbsp;a/3=b/7= 4a + 5b/Q nbsp; ⇒a/3=4× a/ 4× 3.=4a/12 ⇒b/7=5× b/ 5× 7=5b/35 ⇒4a/12=5b/35=4a+5b/12+35 (Using theorem of equal ratios) ⇒a/3=b/7=4a+5b/4 ...

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Byju's Answer

Standard IX

Mathematics

Theorems on Equal Ratios

If a/3=b/7= 4...

Question

If $\frac{a}{3} = \frac{b}{7} = \frac{4 a + 5 b}{Q}$ . Find the value of Q?

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Solution

Given $\frac{a}{3} = \frac{b}{7} = \frac{4 a + 5 b}{Q}$
$\Rightarrow \frac{a}{3} = \frac{4 \times a}{4 \times 3.} = \frac{4 a}{12}$

$\Rightarrow \frac{b}{7} = \frac{5 \times b}{5 \times 7} = \frac{5 b}{35}$

$\Rightarrow \frac{4 a}{12} = \frac{5 b}{35} = \frac{4 a + 5 b}{12 + 35}$ (Using theorem of equal ratios)
$\Rightarrow \frac{a}{3} = \frac{b}{7} = \frac{4 a + 5 b}{47}$
Hence Q = 47.

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If a3=b7=4a+5bQ. Find the value of Q?

Given a3=b7=4a+5bQ ⇒a3=4×a4×3.=4a12 ⇒b7=5×b5×7=5b35 ⇒4a12=5b35=4a+5b12+35 (Using theorem of equal ratios) ⇒a3=b7=4a+5b47 Hence Q = 47.

If $\frac{a}{3} = \frac{b}{7} = \frac{4 a + 5 b}{Q}$ . Find the value of Q?