Ex 3.3, 3
Form the pair of linear equations for the following problems and find their solution by substitution method.
(v) A fraction becomes 9/11 , if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6 . Find the fraction.
Let Numerator be x
& Denominator be y
So, fraction is 𝒙/𝒚
Given that
If 2 is added to both the numerator and the denominator, fraction becomes 9/11
(𝑵𝒖𝒎𝒆𝒓𝒂𝒕𝒐𝒓 + 𝟐)/(𝑫𝒆𝒏𝒐𝒎𝒊𝒏𝒂𝒕𝒐𝒓 + 𝟐)=𝟗/𝟏𝟏
(𝑥 + 2)/(𝑦 + 2)=9/11
11(x + 2) = 9(y + 2)
11x + 22 = 9y + 18
11x – 9y = 18 − 22
11x – 9y = −4
Also,
Given that if 3 is added to both the numerator and the denominator, fraction becomes 5/6
(𝑵𝒖𝒎𝒆𝒓𝒂𝒕𝒐𝒓 + 𝟑)/(𝑫𝒆𝒏𝒐𝒎𝒊𝒏𝒂𝒕𝒐𝒓 + 𝟑)=𝟓/𝟔
(𝑥 + 3)/(𝑦 + 3)=5/6
6(x + 3) = 5(y + 3)
6x + 18 = 5y + 15
6x – 5y = 15 − 18
6x – 5y = −3
Hence, our equations are
11x – 9y = −4 …(1)
6x – 5y = −3 …(2)
From (1)
11x – 9y = −4
11x = 9y – 4
x = ((𝟗𝒚 − 𝟒)/𝟏𝟏)
Putting x in (2)
6x – 5y + 3 = 0
6 ((9𝑦 − 4)/11) – 5y + 3 = 0
Multiply both sides by 11
11 ×(6 (9𝑦 − 4))/11 −5𝑦×11+3×11=0×11
6(9y – 4 ) – 55y + 33 = 0
6(9y) – 6(4) – 55y + 33 = 0
54y – 24 – 55y + 33 = 0
–y + 9 = 0
y = 9
Putting y = 9 in (1)
11x – 9y = −4
11x – 9(9) = −4
11x – 81 = −4
11x = −4 + 81
11x = 77
x = 77/11
x = 7
Therefore x = 7, y = 9
So,
Numerator = x = 7
Denominator = y = 9
Hence,
Original fraction = 𝑁𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟/𝐷𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
"= " 𝑥/𝑦
=𝟕/𝟗

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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