To finish the work in 10 months, number of men required = 480
To finish the work in 1 month, number of men required = 480 x 10
To finish the work in 8 months, number of men required = \(480\times10\over8\)
\(={60\times10\over 1}=600\)
∴ Number of extra men required
= 600 - 480 = 120
Thus, to complete the work in 8 months, 120 extra men are to be employed.

Let the required numbers be 4x and 5x
∴ According to the condition,
\({4x-9\over5x-9}={3\over4}\)
⇒ 4(4x - 9) = 3(5x - 9)
⇒ 16x - 36 = 15x - 27
⇒ 16x - 15x = -27 + 36 or x=9
∴ 4x = 4 x 9 = 36
5x = 5 x 9 = 45
Hence, the required numbers are 36 and 45.

The corresponding fractions of the ratios (2 : 3 and  3 : 4) are \({3\over3}\) and \(3\over 4\)
Now,  \({2\over 3}={2\over 3}\times{4\over 4}={8\over 12}\)     [∵ LCM of 3 and 4 is 12]
and  \({3\over 4}={3\over 4}\times{3\over 3}={9\over 12}\)
Since 8 < 9
or \({{8\over 12}}<{9\over 12}\) or \({2\over 3}<{3\over 4}\)
Thus, 2 : 3 and 3 : 4 are not equivalent.

(a) Rupesh scored 350 out of 500 in 1st term. in II^nd term he scored 80% of 500.
\(\therefore\)His marks in II^nd term =\(\frac { 80 }{ 100 } \)x 500
= 400
\(\therefore\) His improvement in marks = 400 - 350
= 50
Hence, he improved by\(\frac { 50 }{ 500 } \)x 100
= 10%
(b) Percentage.
(c) Hard work is the key to success.

(a) Mr. Narayan saves 20% of his salary
\(\therefore\) His expense = 100 - 20 = 80%
\(\Rightarrow\) His expense = 20,000 x \(\frac { 80 }{ 100 } \)
= Rs. 16,000
(b) Percentage.
(c) Value: Saving is very important.

The parts which the 3 boys are getting is 2 : 3 : 5.
Total of their parts = 2 + 3 + 5 = 10
To get %
Ravi gets =\(\frac { 2 }{ 10 } \times 100\)%=20%
Raju gets =\(\frac { 3 }{ 10 } \times 100\)%=30%
Roy gets =\(\frac { 5 }{ 10 } \times 100\)%=50%
To get amounts:
Ravi gets =\(\frac { 2 }{ 10 } \times 250\)=Rs.50
Raju gets=\(\frac { 3 }{ 10 } \times 250\)=Rs.75
Roy gets=\(\frac { 5 }{ 10 } \times 250\)=Rs.125

In ratio, we would write this as
Rice : Urad dal = 2 : 1
= 2 + 1 = 3 total parts
Now, thi s means \(\frac { 2 }{ 3 } \)X100%
=\(\frac { 200 }{ 3 } =66\frac { 2 }{ 3 } \)%
and,  urad dal in % =\(\frac { 1 }{ 3 } \times 100\)% = 33 \(\frac { 1 }{ 3 } \)%

Total of parts = 3 + 2 = 5
\(\Rightarrow \) Son got = \(\frac { 3 }{ 5 } \)part
\(\Rightarrow \) So his percentage share =\(\frac { 3 }{ 5 } \)X 100=60%
His daughter got=\(\frac { 2 }{ 5 } \) part
So, her percentage share =\(\frac { 2 }{ 5 } \)X100=40%

Let C.P be x
S.P=Rs.280
Profit = 5%
S.P' = C.P. + Profit
\(\Rightarrow \) 280 = x + 5% of x
\(\Rightarrow \) 280= \(x+\frac { 5 }{ 100 } x\)
=\(x+\frac { x }{ 20 } \)
\(\Rightarrow \) 280=\(\frac { 21x }{ 20 } \)
thus, \(x=\frac { 280\times 20 }{ 21 } =\frac { 800 }{ 3 } \)
= 266.66
\(\therefore \) C.P. of article =Rs.266.66.

P = Rs.90000
R = 5·5
T = 3 years
S.L=\(\frac { P\times R\times T }{ 100 } \)
=\(\frac { 90000\times 5.5 }{ 100 } \times 3\)
= 90 x 55 x 3
= Rs.14850
Amount, A = P + S.I
= 90000 + 14850
= 104850
Amount, A= Rs. 104850

Given, CP of a cupboard = Rs 2500
SP of a cupboard = Rs 3000
Since, CP < SP, then
Profit = SP - CP = Rs (3000 - 2500) = Rs 500
So, profit % = \(({Profit\over CP}\times 100)\%=({500\over2500}\times100)\%\)
\({500\over25}\%\)= 20%

Pass percentage = 40%
Total marks of examination = 200
Student got marks = 48
Passing marks = 40% of 200
\(={40\over100}\times200 \\ =40\times 2=80 marks\)
\(\therefore\)  Percentage of marks got by student
\(={48\over200}\times100=24\%\)
Hence, student needed atleast = 80 - 48
= 32 marks to pass the examination.

Let the present age of Aman and her mother be
3x and 11 x.
According to the question,
11 x - 3x = 24 \(\Rightarrow\) 8x = 24\(\Rightarrow\) x = 3
So, Aman's present age = 3x = 3 x 3 = 9 yr
Aman's mother present age = 11 x 3 = 33 yr
After 3 yr, the age of Aman and her mother will be
9 + 3 = 12 yr and 33 + 3 = 36 yr respectively.
\(So, Ratio ={12\over36}={1\over3}=1:3\)

Given, 30% of it is 900 km.
Let x be the kilometre distance.
So, 30% of x = 900 km
\(\frac { 30 }{ 100 } \) x x = 900 ⇒ \(\frac { 30x }{ 100 } \) = 900
30x = 900 x 100
x = \(\frac { 900\times 100 }{ 30 } \)= \(\frac { 9000 }{ 3 } \) = 3000
x = 3000km

Given, ratio 3 : 2
For 3 : 2 of 350,
Sum of ratio = 3 + 2 = 5
So, \(\frac { 3 }{ 5 } \) of 350 = \(\frac { 3 }{ 5 } \)x 350 = 3 x 70 = 210
and \(\frac { 2 }{ 5 } \) of 350 = \(\frac { 2 }{ 5 } \) x 350 = 2 x 70 = 140
∴  3 : 2 of 350 is 210, 140.

Let x%of Rs.80 is Rs.100.
∴ \(\frac { x }{ 100 } \)x80 =100
x= \(\frac { 100\times 100 }{ 80 } \) =\(\frac { 10000 }{ 80 } \)   ⇒   x =125%
Hence, 125% of 80 is Rs.100.

Let x%of 1 h is 30 min.
So,  \(\frac { x }{100} \) x1 h = 30min
∴ \(\frac { x }{100} \) x 60min = 30 min  [∵ 1 h =60 min]
x = \(\frac { 30 ｘ100 }{60} \)
⇒   x =\(\frac { 100 }{ 2 } \) = 50%
Hence, 50% of 1 his 30 min

Rs 24500

Given, CP of a book = Rs 275; Loss per cent = 15%
\(\therefore\) Loss = 15% of CP
=  \({15\over100} \times 275 = {4125 \over 100}\) = Rs 41.25
Now, SP of a book = CP - Loss = Rs(275 - 41.25)
= Rs 233.75
Hence, Amina sells the book for Rs 233.75

We have, Rs  5 to 50 paise
We know that, Rs 1= 100 paise = 5 x 100 paise = 500 paise
\(\therefore\) Required ratio = Rs 5: 50 paise = 500 paise: 50 paise
=500:50=\({500\over50}={50\over5}={10\over1}or10:1\)