the sum of the numerator and denominator of a fraction is 12
Mohammed
Guys, does anyone know the answer?
get the sum of the numerator and denominator of a fraction is 12 from screen.
The sum of the numerator and the denominator of a fraction is 12 . If the denominator is increased by 3 , the fraction becomes 1 / 2. Find the fractions.
The sum of the numerator and the denominator of a fraction is 12 . If the denominator is increased by 3 , the fraction becomes 1 / 2. Find the fractions.
Byju's Answer Standard X Mathematics
Elimination Method of Finding Solution of a Pair of Linear Equations
The sum of th... Question
The sum of the numerator and the denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fractions.
Open in App Solution
Let numerator = x and denominator = y
From the given conditions, we have:
x + y = 12 ... (1) x/y+3 = 1/2 2x - y = 3 ... (2)
Adding (1) and (2), we get,
3x = 15 or x = 5 So, y = 12 - 5 = 7
Thus, the fraction is 5/7.
Suggest Corrections 32
SIMILAR QUESTIONS
Q. The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.Q.The sum the numerator and denominator of a fraction is 12 if the denominator is increased by 3 the fraction becomes 1\2 find the fraction
Q.The sum of the numerator and denominator of a fraction is 12. If the denominator is incresed by 3, the fraction becomes 1/2. Find the fraction.
Q. Sum of the numerator and the denominator of a fraction is 12. If the denominator is increared by 3 then fraction becomes 1/2. Find the fraction.Q. In a fraction, if numerator is increased by 2 and denominator is decreased by 3, then the fraction becomes 1. Instead, if numerator is decreased by 2 and denominator is increased by 3, then the fraction becomes3 8
. Find the fraction.
View More RELATED VIDEOS
Algebraic Solution MATHEMATICS Watch in App EXPLORE MORE
Elimination Method of Finding Solution of a Pair of Linear Equations
Standard X Mathematics
The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.
Q.11 of chapter 3, 3. Pair of Linear Equations in Two Variables - RD Sharma - Mathematics book. The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.
11
The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.
Let the numerator be ‘a’ and denominator be ‘b’.
Given, sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2.
⇒ a + b = 12 ------ (1)
Also, a/(b + 3) = 1/2
⇒ 2a – b = 3 ------- (2)
Adding eq1 and eq2
⇒ a + b + 2a – b = 15
⇒ 3a = 15 ⇒ a = 5 Thus, b = 7 Fraction is 5/7.
The Sum of the Numerator and Denominator of a Fraction is 12. If the Denominator is Increased by 3, the Fraction Becomes 1/2. Find the Fraction.
The Sum of the Numerator and Denominator of a Fraction is 12. If the Denominator is Increased by 3, the Fraction Becomes 1/2. Find the Fraction.
Advertisement Remove all ads Ads by Definition
The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.
Advertisement Remove all ads
SOLUTION
Let the numerator and denominator of the fraction be x and y respectively. Then the fraction is
xy
The sum of the numerator and denominator of the fraction is 12. Thus, we have
x+y=12 ⇒x+y-12=0
If the denominator is increased by 3, the fraction becomes
12 . Thus, we have xy+3=12 ⇒2x=y+3 ⇒2x-y-3=0
So, we have two equations
x+y-12=0 2x-y-3=0
Here x and y are unknowns. We have to solve the above equations for x and y.
By using cross-multiplication, we have
x1×(-3)-(-1)×(-12)=-y1×(-3)-2×(-12)=11×(-1)-2×1
⇒x-3-12=-y-3+24=1-1-2
⇒x-15=-y21=1-3 ⇒x15=y21=13 ⇒x=153,y=213 ⇒x=5,y=7
Hence, the fraction is
57
Concept: Equations Reducible to a Pair of Linear Equations in Two Variables
Is there an error in this question or solution?
Chapter 3: Pair of Linear Equations in Two Variables - Exercise 3.8 [Page 89]
Q 11 Q 10 Q 1
APPEARS IN
RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.8 | Q 11 | Page 89
VIDEO TUTORIALSVIEW ALL [3] view
Video Tutorials For All Subjects
Equations Reducible to a Pair of Linear Equations in Two Variables
video tutorial 00:14:35
Equations Reducible to a Pair of Linear Equations in Two Variables
video tutorial 00:08:41
Equations Reducible to a Pair of Linear Equations in Two Variables
video tutorial 00:17:17
Guys, does anyone know the answer?