### Question 3

SSC-CGL 2020 Mar 4 Shift 1

If numbers (2x+1), (x+2), 2 and 5 are in proportion, then mean proportion of 3.5(1-x) and 8(1+x) is?

### Solution in Detail

Def [NCERT class VI Math]: if a, b. c. d are in proportion, then ratio of a to b is equal to the ratio of c to d.Given $\displaystyle \frac{2x + 1}{x + 2} = \frac{2}{5}$

After solving, $\displaystyle x = -\frac 18$

First we calculate $\displaystyle 3.5 (1 - x) $$\displaystyle = 3.5 [1 - (-1/8)] = \frac {63}{16}$

Similarly we can calculate $\displaystyle 8 (1 + x)$

$\displaystyle = 8 [1 + (-1/8)] = 7$

Mean proportion of a and b is square root of the product of ab.$\displaystyle \therefore \sqrt{3.5 (1 - x) \cdot 8(1 + x)}$

$\displaystyle = \sqrt{\frac{63}{16} \times 7} = \sqrt{\frac{7 \times 9}{16} \times 7}$

$\displaystyle = \frac{7 \times 3}{4} = \frac{21}{4}\:\underline{Ans}$

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