Question

2. The sum of the numerator and denominator of a certain fraction is 10. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by2/21 Find the fraction.

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Answer 1

Answer:

let the fraction

x\y

Case 1

x+y=10

Case 2

x-1/y-1=2/21

now solve the equation by any of three method

Step-by-step explanation:

hope it helps

Answer 2

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Q - The sum of the neumerator & denominator of a certain fraction is 10 . If 1 is subtracted from both the neumerator and denominator , the fraction is decreased by $\dfrac{2}{21}$ . Find the fraction .

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★ Concept :

• The top number in a fraction represents neumerator .

• The bottom number in a fraction represents denominator .

• The fraction is usually represented in simplified form .

• Simplified form means , the H.C.F. of the neumerator and denominator must be 1 .

★ We have :

• neumerator + denominator = 10
• 1 is subtracted from the fraction
• new fraction = $\dfrac{n}{d}-\dfrac{2}{21}$

★ To Find :

• What was the original fraction ?

★ Solution :

• Let neumerator be "n"
• and denominator be "d"

$\rm \: fraction \: = \frac{n}{d}$

and

$\rm \: n \: + \: d = 10$

so ,

$\rm \mapsto \: n = 10 - d.....(i)$

$\therefore \rm \: fraction = \frac{10 - d}{d}$

Now ,

According to the Question -

$\mapsto \rm \: \frac{n - 1}{d - 1} = \frac{n}{d} - \frac{2}{21}$

from eq (i) ,

$\mapsto \rm \: \frac{10 - d - 1}{d - 1} = \frac{10 - d}{d} - \frac{2}{21}$

$\mapsto \rm \: \frac{9 - d}{d - 1} = \frac{21(10 - d) - 2d}{21d}$

$\mapsto \rm \: \frac{9 - d}{d - 1} = \frac{210 - 21d - 2d}{21d}$

$\mapsto \rm \: \frac{9 - d}{d - 1} = \frac{210 - 23d}{21d}$

cross Multiply

$\mapsto \rm \: (9 - d)21d = (d - 1)(210 - 23d)$

$\mapsto \rm \: 189d - 21 {d}^{2} = 210d - 210 - 23 {d}^{2} + 23d$

$\mapsto \rm \: 189d - 21 {d}^{2} = 233d - 23 {d}^{2} - 210$

$\mapsto \rm \: 23 {d}^{2} - 21 {d}^{2} + 189d - 233d + 210 = 0$

$\mapsto \rm \: 2 {d}^{2} - 44d + 210 = 0$

$\mapsto \rm \: {d}^{2} - 22d + 105 = 0$

$\mapsto \rm \: {d}^{2} - 15d - 7d + 210 = 0$

$\mapsto \rm \: d(d - 15) - 7(d - 15) = 0$

$\mapsto \rm \: (d - 7)(d - 15) = 0$

So ,

$\rm \: either \: \boxed{ \rm \: d = 7} \: or \: \boxed{ \rm \: d = 15}$

15 is rejected as , we know that n + d = 10 so ,

d can't be greater than 10

So ,

$\boxed{ \rm \: d = 7}$

put in eq (i)

${ \rm \: n = 10 - 7}$

$\boxed{ \rm \: n = 3}$

So ,

The fraction would be

$\large\boxed{ \rm \: fraction = \frac{3}{7} }$

So , This is the required answer !!