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.

5 em represent 1000 Ian.
∴ 1 em will represent \({1000\over 5}\)km.
2.5 em WIll represent \({1000\over 5}\times{25\over10}=500km\)

(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.

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 \(\frac { 1 }{ 3 } \)%

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%

Amount divided between A and B is in the ratio 7: 9.
B's share = Rs 7200
B's share in ratio = \({9\over7+9}={9\over16}\)
Let total amount be Rs x.
According to the question,
\({9\over16}\times \times =7200\)
\( x={7200\times 16\over9}=800\times16=Rs12800\)
 Hence, Total amount is Rs. 12800

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, percentage of students having bicycle = 65%
This means that if there were 100 students in a class, out of them, 65 would have bicycles and then remaining students would not have bicycles.
\(\therefore\)The remaining students would not have bicycle
= 100 - 65 = 35
Hence, 35% of students do not have bicycles.

CP of 10 egg =Rs 8 
\(\Rightarrow cp \ 1 \ egg =Rs {8\over10}=Rs{4\over5}\)
SP of 8 eggs = Rs10
SP of 1 egg = \(Rs {10\over8}=Rs{5\over4}\) i.e. SP is greater than CP.
\(Since, {5\over4}>{4\over5},\)           \([\because {5\over4}={5\times4\over5\times4}={25\over20} and {4\over5}={4\times5\over5\times4}={16\over20}]\)
Therefore, there is a gain
Gain=SP of 1egg-CP of 1egg = Rs\(\left({5\over4}-{4\over5}\right)=Rs{9\over20}\)
Gain % =\(\begin{pmatrix} {Gain\over CP}\times100) \end{pmatrix}\%=\begin{pmatrix} {{9\over20}\over{4\over5}}\times100 \end{pmatrix} \%=\left({9\over20}\times{5\over4}\times100\right)\%=({225\over4})\%=56.25\%\)

We have, 9 m to 27 cm
We know that,
1 m = 100 cm \(\Rightarrow\) 9 m = 9 X 100 cm = 900 cm
\(\therefore\)Required ratio = 9 m: 27 cm = 900 cm: 27 cm
\(=900:27={900\over27}={100\over3}or 100:3\)

We have, 15 kg to 210 g
We know that, 1 kg = 1000 g
15 kg = 15 X 1000 g = 15000g
\(\therefore\) Required ratio = 15 kg: 210 g = 15000 g: 210 g
=15000:210\(={15000\over210}={1500\over21}={500\over7}or 500:7\)