Question

Find x, if 17, x, 20, and 40 are in proportion.

Answer 1

$\huge{\underline{\underline{\red{\sf{Given}}}}}\:{\red{:}}$

• $\sf{17\::\:x\::\:20\::\:40}$

${ }$

$\huge{\underline{\underline{\red{\sf{Find}}}}}\:{\red{:}}$

• $\sf{Find\:the\:value\:of\:x}$

${ }$

$\huge{\underline{\underline{\red{\sf{Solution}}}}}\:{\red{:}}$

$\:\:\:\:\:\:\:\leadsto{\sf{17\::\:x\::\:20\::\:40}}$

$\:\:\:\:\:\:\:\leadsto{\sf{\frac{17}{x}}\:={\frac{20}{40}}}$

$\:\:\:\:\:\:\:\leadsto{\sf{20x\:=\:17\:\times\:40}}$

$\:\:\:\:\:\:\:\leadsto{\sf{20x\:=\:680}}$

$\:\:\:\:\:\:\:\leadsto{\sf{x\:=\:{\frac{\cancel{680}}{\cancel{20}}}}}$

$\:\:\:\:\:\:\:\leadsto{\sf{x\:=\:34}}$

${ }$

$\:\:\:\:\:\:\:\:\:\:\:\small{\therefore\:{\underline{\sf{Hence,\:the\:value\:of\:x\:is\:{\bold{34}\:.}}}}}$

Answer 2

Solution:-

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$\large\to{\underbrace{\underline{\sf{Understanding\:the\:concept:-}}}}$

Here the question has asked us to find out the value of x. To find x we will follow the method of product of means and product of extreme. Then we will get the answer.

ANSWER:-

✓ Value of x is 34.

GIVEN:-

» 17:x :: 20 : 40

TO FIND:-

➲ Value of x in 17:x :: 20:40

FORMULA:-

✧ Value of x = (Product of means = Product of extremes)

SOLUTION:-

$\maltese \: \: \underbrace{\sf a\ :\underbrace{ b\ ::\ c}\ : d}$

$\maltese \: \: \underbrace{\sf 17\ :\underbrace{\sf x\ ::\ 20}\ : 40}$

$\maltese \: \:{\sf {\underbrace{\sf x\ ::\ 20}} = Product \: of \: means}$

$\maltese \: \: {\sf { \underbrace{17 \ :\ 40}} = Product \: of \: extremes}$

$\dag \: { \sf{20 \times x = 17 \times 40}}$

$\dag \: { \sf{20x =680}}$

$\dag \: { \sf{x =680 \div 20}}$

$\dag \: { \sf{x =680 \div 20 = 34}}$

$\dag \: { \sf{x =34}}$

VERIFICATION:-

• L.H.S

➤ 20 × 34

➤ 20 × 34 = 680

➤ 680

➤ L.H.S is 680.

• R.H.S

➤ 17 × 40

➤ 17 × 40 = 680

➤ 680

➤ R.H.S is 680

➤680 = 680

∴ L.H.S = R.H.S

• They are in proportion.

Hence, verified.

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