If x-3 - 2-5-3-4 - 2x - 16-15- then value of x is equal to

The correct option is B 18 37 Given, x 3 2 5 #160; 3 4 2x = 16 15 ⟹ 5x 6 15 #160; 3 8x 4 #160; = 16 15 ⟹ 5x 6 15 × 4 ...

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Byju's Answer

Standard VI

Mathematics

Construction of a Circle with Known Radius

If x/3 - 2/...

Question

If $\frac{\frac{x}{3} - \frac{2}{5}}{\frac{3}{4} - 2 x} = \frac{16}{15}$ , then value of $x$ is equal to

\frac{11}{13}

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\frac{18}{37}

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\frac{21}{8}

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\frac{1}{4}

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Solution

The correct option is B $\frac{18}{37}$
Given,
$\frac{\frac{x}{3} - \frac{2}{5}}{\frac{3}{4} - 2 x} = \frac{16}{15} ⟹ \frac{\frac{5 x - 6}{15}}{\frac{3 - 8 x}{4}} = \frac{16}{15} ⟹ \frac{5 x - 6}{15} \times \frac{4}{3 - 8 x} = \frac{16}{15} ⟹ (5 x - 6) \times \frac{1}{3 - 8 x} = 4 ⟹ 5 x - 6 = 4 (3 - 8 x) [O n c r o s s - m u l t i p l i c a t i o n] ⟹ 5 x - 6 = 12 - 32 x ⟹ 5 x + 32 x = 12 + 6 [T r a n s p o s i n g - 32 x t o L H S a n d - 6 t o R H S] ⟹ 37 x = 18 ⟹ x = \frac{18}{37}$

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(i)

\frac{11}{12} \div (\frac{5}{9} \times \frac{18}{25})

(ii)

(2 \frac{1}{2} \times \frac{8}{10}) \div (1 \frac{1}{2} + \frac{5}{8})

(iii)

\frac{15}{16}

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(iv)

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(v)

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(vi)

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Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$