Let the numerator and denominator be p and q respectively.
Then, (p + 2) / (q + 3) = 7/9
? 9(p + 2) = 7(q +3)
? 9p - 7q = 3 ....(i)
Again, (p - 1) / (q - 1) = 4/5
? 5p - 4q = 1 ....(ii)
Solving (i) and (ii) we get,
p = 5, q = 6
Required fraction = 5/6
Let the original fraction be p/q
Then, (p + 2) / (q + 1) = 5/8
? 8p - 5q = 11 .....(i)
Again (p + 3) / (q + 1) = 3/4
? 4p - 3q = 9 ...(ii)
Solving equations , (i) and (ii), we get ,
p = 3 and q = 7
? Fraction = 3/7
Let the required fraction be p/q
? p / (q + 3) = 1/3
? 3p - q = 3 ...(i)
and, (p + 4) / q = 3/4
? 4p - 3q = -16 ...(ii)
Solving these equations, we get p = 5, q = 12
? Required fraction = 5/12
Given Expression = (.53)3 - (.42)3- 3 x .58 x .42 x (.58-.42)
= a3-b3 -3ab(a - b)
= (a - b)3
(where a = .58 and b=.42)
= (.58 - .42 )3
= .16 x .16 x .16
= 0.004096
Given expression =(.6)3 + (.4) 3 + 3 x .6 x .4 x (.6 + .4)
= a3 + b3 + 3ab (a+b)
= (a+b)3
= (.6 + .4)3
= 13
= 1
2/5 = 0.4 , 5/6 = 0.833, 11/12 = 0.916 and 7/8 = 0.875
Clearly, the greatest fraction is 0.916, i, e . 11/12.
Let the numerator and denominator be p and q respectively.
Then, (p + 2) / (q + 3) = 7/9
? 9(p + 2) = 7(q +3)
? 9p - 7q = 3 ....(i)
Again, (p - 1) / (q - 1) = 4/5
? 5p - 4q = 1 ....(ii)
Solving (i) and (ii) we get,
p = 5, q = 6
Required fraction = 5/6
Given expression = [(32)2 x (3 x 3 x 2)4] / 316
= (34 x 38 x 24) / 316
= 24 / 34 = 16 / 81
Let man's salary be Rs. N
Money spend on food =N/7
Money spends on clothing = (N - N/7) x 1/2 = (6N/7) x (1/2) =3N/7
Money spend on entertainment = (N - N/7 - 3N/7)/3 = (7N - 4N)/7 = N/7
Now, money left =600
? N - N/7 - 3N/7 - N/7 = 600
? 7N - 5N/7 = 600
? N = 600 x 7/2 = Rs. 2100
? Money spend on entertainment = 1/7 x 2100 = Rs. 300
If the required fraction be N.
Then, (N x N) / (1/N) = 1826/27
? N3 = 512 / 27
? N = 8/3 = 22/3
Let the length of lamppost = L m
Then,first part = L/3
and second part = (3/8) x L/3 = L/8
and third part = 6 m 50 cm = 6.50 m
First part + second part + Third part = length of lamppost
? L/3 + L/8 + 6.5 = L
? L - L/3 - L/8 =6.5
? (24L - 8L - 3L)/24 = 6.5
? 13L/24 = 6.5
? L = (65.x 24)/13 = 12 m
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