Please help me solving all
Answers
Question 1 :
Let the two no.s be x and 2 x.
x + 2 x = 60
= > 3 x = 60
= > x = 20
Hence no.s are 20 and 40
ANSWER : 20 and 40
Question 2 :
3 + 2x = 5/x
= > 3 x + 2 x² = 5
= > 2 x² + 3 x - 5 = 0
= > 2 x² - 2 x + 5 x - 5 =0
= > 2 x ( x - 1 ) + 5 ( x - 1 ) =0
x - 1 = 0
or 2 x + 5 = 0
x = 1 or x = -5/2
ANSWER : 1 or -5/2
Question 3 :
Let no. be x .
x + 32 = 3 x
= > 2 x = 32
= > x = 16
ANSWER : The number is 16 .
Question 4 :
Let no.s be x and x+1
x + x + 1 = 55
= > 2 x + 1 = 55
= > 2 x = 54
= > x = 27
x + 1 = 28
28 is greater
ANSWER : 28
Question 5 :
Let the no. be x
2 x + 12 = 50
= > 2 x = 50 - 12
= > 2 x = 38
= > x = 38/2
= > x = 19
ANSWER :
19
Question 6 :
Let no.s be x , x + 2 , x + 4
x + x + 2 + x + 4 = 225
= > 3 x = 225-6
= > 3 x = 219
= > x = 73
x + 2 = 75
x + 4 = 77
ANSWER : 73 , 75 , 77.
Question 7 :
The no.s are x , x + 3 , x + 6
x + x + 3 + x + 6 = 315
= > 3 x = 315-9
= > x = 306/3
= > x = 102
ANSWER 102, 105 , 108
Question 9 :
Let the fraction be ( x - 7 ) / x
According to problem :
( x - 7 )/x = ( x - 7 + 2 ) / ( x + 9 )
= > ( x - 7 ) ( x + 9 ) = x ( x - 5 )
= > x² - 7 x + 9 x - 63 = x² - 5 x
= > x² - 2 x - 63 = x² - 5 x
= > 3 x = 63
= > x = 63/3
= > x = 21
Fraction = ( 21 - 7 ) / 21 = 14/21
ANSWER : 14/21
Q: 1 :
Solution:
Let the two number be k and 2k.
k + 2k = 60
⇒ 3k = 60
⇒ k = 20
Therefore, 2 numbers are 20 and 40
Q: 2 :
Solution:
3 + 2k = 5/k
= > 3k + 2k² = 5
= > 2k² + 3k - 5 = 0
= > 2k² - 2k + 5k - 5 =0
= > 2k ( k - 1 ) + 5 ( k - 1 ) =0
k - 1 = 0
or, 2k + 5 = 0
k = 1 or k = -5/2
Q: 3 :
Solution:
Let no. be k .
k + 32 = 3k
= > 2k = 32
= > k = 16
Hence, The number is 16 .
Q: 4 :
Solution:
Let no.s be k and k+1
k + k + 1 = 55
= > 2k + 1 = 55
= > 2k = 54
= > k = 27
k + 1 = 28
Hence, 28 is greater
Q: 5 :
Solution:
Let the no. be k
2k + 12 = 50
= > 2k = 50 - 12
= > 2k = 38
= > k = 38/2
= > k = 19
Hence, the number is 19
Q:6 :
Let numbers be k , k + 2 , k + 4
k + k + 2 + k + 4 = 225
= > 3k = 225-6
= > 3k = 219
= > k = 73
k + 2 = 75
k + 4 = 77
Hence, the numbers are: 73 , 75 and , 77.
Q: 7 :
Solution:
The numbers be k , k + 3 , k + 6
k + k + 3 + k + 6 = 315
= > 3k = 315-9
= > k = 306/3
= > k = 102
Hence, numbers are 102, 105 and , 108
Q: 9 :
Solution:
Let the fraction be ( k - 7 ) / k
According to problem :
( k - 7 )/k = ( k - 7 + 2 ) / ( k + 9 )
= > ( k - 7 ) ( k + 9 ) = k ( k - 5 )
= > k² - 7 k + 9 k - 63 = k² - 5 k
= > k² - 2 k - 63 = k² - 5 k
= > 3 k = 63
= > k = 63/3
= > k = 21
Hence, Fraction is ( 21 - 7 ) / 21 = 14/21