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Question 166. The sum of two number is 18 and the sum of their reciprocals is 1/4.Find the number, by Ujjawal. Answered on June 20, 2008 at 11:35PM
Answer 166 Let the numbers be x and 18 - x
according to problem
1/x + 1/(18 - x) = 1/4
x^2 - 18 x + 72 = 0
(x - 12) (x - 6) = 0
x = 12 or x = 6
If x = 12 the first number = 12 and second number = 6
If x = 6 the first number = 6 and second number = 12
therefore the numbers are 6 and 12
Question 167. Rationalise the denominator 4/(2+root3+root7) by Karan Batra. Answered on June 27, 2008 at 5:48 p.m.
Answer 167. 4/(2+root3+root7) × (2+root3 - root7) /(2+root3 - root7)
= 4(2 + root3 - root7)/ [(2+root3)^2 - (root7)^2]
= 4(2 + root3 - root7)/ [4 + 3 + 4root3 - 7]
= 4(2 + root3 - root7)/ 4root3
= (2 + root3 - root7)/ root3
= (2 + root3 - root7)/ root3 × root3 / root3
= root3(2 + root3 - root7)/ 3
Question 168. Solve sec^2 10 - cos^2 80 by sidharth. Answered on July 6, 2008 at 12:01 a.m.
Answer 168. sec^2 10 - cos^2 80
= cos^2 (90 - 10) - cos^2 80
= cos^2 80 - cos^2 80
= 0
Question 169. Form the pair of linear equations for the following problem & find their solution by substitution method.
A fraction becomes 9/11, if 2 is added to both the numerator & the denominator. If 3 is added to both the numerator & the denominator it becomes 5/6 . Find the fraction, by Shakti Singh Delhi. Answered on July 15, 2008 at 10:40 p.m.
Answer 169. Let numerator = x and denominator = y
fraction = x/y
according to condition 1
(x + 2)/(y + 2) = 9/11
11x + 22 = 9y + 18
11x - 9y = - 4 ......................(i)
according to condition 2
(x + 3)/(y + 3) = 5/6
6x + 18 = 5y + 15
6x = 5y - 3
x = (5y - 3)/6 ..................... (ii)
Substituting value of x from ii in i
11[(5y - 3)/6 ] - 9y = -4
(55y - 33)/6 - 9y = - 4
55y - 33 - 54y = - 24
y = 9
Substituting value of y in ii
x = (5×9 - 3)/6
x = 42/6
x = 7
Therefore required fraction = 7/9
Question 170. The sum of digits of a two digit number is 13.If the number is subtracted from one obtained by interchanging the digits,the result is 45 .what is the number by Robin Prasad, Varanasi. Answered on July 18, 2008 at 9:44 p.m.
Answer 170. Let digit at units place = x
digit at tens place = y
Number = 10y + x
Number formed by interchanging the digits = 10x + y
condition 1 10x + y - (10y + x) = 45
10x + y - 10y - x = 45
9x - 9y = 45
x - y = 5 ...............(i)
condition 2 x + y = 13 ................(ii)
(i) + (ii)
2x = 18
x = 9
Substituting in (i)
9 - y = 5
y = 4
Given No. = 49
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Answer 166 Let the numbers be x and 18 - x
according to problem
1/x + 1/(18 - x) = 1/4
x^2 - 18 x + 72 = 0
(x - 12) (x - 6) = 0
x = 12 or x = 6
If x = 12 the first number = 12 and second number = 6
If x = 6 the first number = 6 and second number = 12
therefore the numbers are 6 and 12
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Answer 167. 4/(2+root3+root7) × (2+root3 - root7) /(2+root3 - root7)
= 4(2 + root3 - root7)/ [(2+root3)^2 - (root7)^2]
= 4(2 + root3 - root7)/ [4 + 3 + 4root3 - 7]
= (2 + root3 - root7)/ root3
= (2 + root3 - root7)/ root3 × root3 / root3
= root3(2 + root3 - root7)/ 3
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Answer 168. sec^2 10 - cos^2 80
= cos^2 (90 - 10) - cos^2 80
= cos^2 80 - cos^2 80
= 0
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A fraction becomes 9/11, if 2 is added to both the numerator & the denominator. If 3 is added to both the numerator & the denominator it becomes 5/6 . Find the fraction, by Shakti Singh Delhi. Answered on July 15, 2008 at 10:40 p.m.
Answer 169. Let numerator = x and denominator = y
fraction = x/y
according to condition 1
(x + 2)/(y + 2) = 9/11
11x + 22 = 9y + 18
11x - 9y = - 4 ......................(i)
according to condition 2
(x + 3)/(y + 3) = 5/6
6x + 18 = 5y + 15
6x = 5y - 3
x = (5y - 3)/6 ..................... (ii)
Substituting value of x from ii in i
11[(5y - 3)/6 ] - 9y = -4
(55y - 33)/6 - 9y = - 4
55y - 33 - 54y = - 24
y = 9
Substituting value of y in ii
x = (5×9 - 3)/6
x = 42/6
x = 7
Therefore required fraction = 7/9
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Answer 170. Let digit at units place = x
digit at tens place = y
Number = 10y + x
Number formed by interchanging the digits = 10x + y
condition 1 10x + y - (10y + x) = 45
10x + y - 10y - x = 45
9x - 9y = 45
x - y = 5 ...............(i)
condition 2 x + y = 13 ................(ii)
(i) + (ii)
2x = 18
x = 9
Substituting in (i)
9 - y = 5
y = 4
Given No. = 49
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Answer 171. Let the no = y
according to problem
y + square root y = 6/25
square root y = x
x^2 + x - 6/25 = 0
25 x^2 +25 x - 6 = 0
(5x + 6)(5x - 1) = 0
x = -6/5, x = 1/5
Putting back the value of x in terms of y
square root y = -6/5 , square root y = 1/5
Squaring both sides
y = 36/25, x = 1/25