Question

the pyramid of number is greater than its numerator by 7 3 subtracted from the numerator and 2 is added to its denominator the new number becomes 1 by 5 find the rational number​

Answer 1

$\bold{\underline{\underline{\huge{\sf{ANSWER:}}}}}$

Given:

The denominator of a rational number is greater than its numerator by 7.If 3 subtracted from the numerator and 2 is added to its denominator the new number becomes 1 by 5.

To find:

The original rational number.

Explanation:

Let the numerator of given rational number be R &

then denominator be (R+7)

∴ The original fraction= $\frac{\bold{R}{R+7}}$

If numerator decreased by 3

→ R-3

If denominator increased by 2

→ R+7+2

→ R+9

∴ New number becomes= 1/5

According to the question:

⇒ $\frac{R-3}{R+9} =\frac{1}{5}$

[cross-multiplication]

⇒ 5(R-3)= 1(R+9)

⇒ 5R - 15= R+9

⇒ 5R -R = 9+15

⇒ 4R = 24

⇒ R= $\frac{\cancel{24}}{\cancel{4}} =6$

Thus,

The original number is $\frac{6}{6+7}$

The original number is 6/13.