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
Given expression = [(32)2 x (3 x 3 x 2)4] / 316
= (34 x 38 x 24) / 316
= 24 / 34 = 16 / 81
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 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
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
27 x 1.2 x 5.5262 x 0.6
= 27 x [(12 - 1) / 9] x [(55262 - 5526)/9000] x (6/9)
= (27 x 11)/9 x (49736/9000) x (6/9)
= 1094192 / 9000
= 121.576888...
= 121.5768
Total length of the rod = 330 cm
Length of a piece = 13.2 cm.
Required number of pieces = Total length/Length of a piece ;
Required number of pieces = 330/13.2 = 25
Let the total length of pencil = L cm
Then, black part = L/8
? Remaining part = L - L/8 = 7L/ 8
and White part = (7L/8)/2 = 7L/8
? Remaining part = L - (L/8 + 7L/16) = 7L/16
? length of blue part = 7L/16
According to the question,
7L/16 = 31/2
? 7L/16 = 7/2
? L =8
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