Question

Six times the denominator of affection islas
than eight times the mumerator ad ten times the
numerator equals 20 less that ten time the
denaminator. The reciprocal of theffationis
(A) 6/7 (B) 38 (C) 719 (0) 97​

Answer 1

CORRECT QUESTION:

Six times the denominator of a fraction is less than eight times the numerator and ten times the numerator equals 20 less than ten times the denominator. The reciprocal of the fraction is

• (A) 6/7
• (B) 3/8
• (C) 7/9
• (D) 9/7

ANSWER:

• The reciprocal of the fraction is 9/7

GIVEN:

• Six times the denominator of a fraction is less than eight times the numerator.

• Ten times the numerator equals 20 less than ten times the denominator.

TO FIND:

• The reciprocal of the fraction.

EXPLANATION:

Let the numerator be x and the denominator be y

6y < 8x

3y < 4x

10x = 10y - 20

x = y - 2

Subtitute x = y - 2 in 3y < 4x

3y < 4(y - 2)

3y < 4y - 8

8 < 4y - 3y

y > 8

Hence denominator should be greater than 8 and if we take reciprocal of the fraction then numerator will be greater than 8.

HENCE OPTION D) IS CORRECT.

VERIFICATION:

Reciprocal = 9/7

Fraction = 7/9

Substitute x = 7 and y = 9 in 10x = 10y - 20

10(7) = 10(9) - 20

70 = 90 - 20

70 = 70

HENCE VERIFIED.