Question

the denominator of a rational number is greater than its numerator by 7.if the numerator is increased by 15 and the denominator is decreased by 2,the number oftained is 5/3.find the rational number.​

Answer 1

Answer:

10/17

Step-by-step explanation:

d=I+7

n+15

d-2

n/n+7=

n+15/n+5=5/3

3n+45=5n+25

2n=20

n=10

d=17

Answer 2

Solution :-

Let :-

Numerator = x

Denominator = y

According to the first condition :-

$\sf y = x+7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x+15}{y-2} = \dfrac{5}{3}\\\\\longrightarrow 3(x+15)= 5(y-2) \\\\\longrightarrow 3x+45=5y-10 \\\\\longrightarrow 3x-5y = -55 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(2)$

Substitute the value of y in eq (2) :-

$\longrightarrow \sf 3x-5(x+7) = -55 \\\\\longrightarrow 3x-5x-35 = - 55 \\\\\longrightarrow 3x-5x = -55+35 \\\\\longrightarrow -2x= -20 \\\\\longrightarrow \bf x = 10$

Substitute x = 10 in eq (1) :-

$\longrightarrow \sf y = 10+7 \\\\\longrightarrow \bf y = 17$

$\bf FRACTION = \dfrac{10}{17}$