1. \(\because\) Cost of 2 handkerchiefs = Rs. 30
\(\therefore\) Cost of 1 handkerchief = Rs. \(\frac { 30 }{ 2 } \) = 15
2. \(\because\) Cost of 3 kg rice = Rs. 600
\(\therefore\) cost of 1 kg rice = Rs. \(\frac { 600 }{ 3 } \)=200
3. \(\because\) Cost of 5 combs = Rs. 30
\(\therefore\) Cost of 1 comb = Rs. \(\frac { 30 }{ 5 } \) = Rs. 6
4. \(\because\) Cost of 12 envelopes = Rs. 60
\(\therefore\) Cost of 1 envelope = Rs. \(\frac { 60 }{ 12 } \) = Rs. 5
5. \(\because\) Cost of 8 postcards = Rs. 8
\(\therefore\)Cost of 1 postcard = Rs. \(\frac { 8 }{ 8 } \) ​​​​​​​= Rs. 1

Given, distance travel by train = 130 km
and time taken by train = 2 h
\(\therefore Speed\ of\ train=\frac{130\ km}{2\ h}=65\ km/h\)
and distance between Delhi to Bhopal = 780 km
Let time taken by train = x h
Then, \(Speed\ of\ train=\frac{Distance\ between\ Bhopal\ to\ Delhi}{Time\ taken\ by\ train}\)
\(\Rightarrow 65=\frac{780}{x}\)
\(\Rightarrow x=\frac{780}{65}=12\ h\)
Hence,the required time is 12 h for distance 780 km.

(a) 1278 km
(b) 19 L

14 : 19

319.64 L

Rs 180, Rs 120

864 km

(a) Here, the quantity of wheat is known and cost is unknown.
Given, cost of 5 kg of wheat = Rs.30.50
\(\therefore\) Cost of 1 kg of wheat \(=Rs.\frac{30.50}{5}=Rs.6.10\)
\(\therefore\) Cost of 8 kg of wheat =Rs.6.10 X 8=Rs.48.80
Hence, the cost of 8 kg of wheat is Rs.48.80.
(b) Here, the cost of wheat is known and quantity of wheat is unknown.
Given, in Rs.30.50 quantity of wheat that can be purchased = 5 kg
\(\therefore\) In Rs.1, quantity of wheat that can be purchased
\(=\frac{5}{30.50}\ kg=\frac{5\times10}{305}\ kg=\frac{50}{305}\ kg \)
[multiplying numerator and denominator both by 10]
\(\therefore\) In Rs.61, quantity of wheat that can be purchased
\(=\frac{50}{305}\times61=\frac{50}{5}\ kg=10\ kg\)
Hence, 10 kg wheat can be purchased in Rs.61.

Rs.468

Given, number of girls = 2300
and total number of students = 4320
\(\therefore\) Number of boys = Total number of students - N umber of girls
= 4320 - 2300 = 2020
(a) Ratio = 115: 216
(b) Ratio = 101: 115
(c) Ratio = 101: 216

Given, money earned by Seema = Rs. 150000
and money saved by Seema = Rs. 50000
(a) \(Required\ ratio=\frac{Money\ earned\ by\ Seema}{Money\ saved\ by\ Seema}\)
\(=\frac{Rs.150000}{Rs.50000}=\frac{15000\div50000}{50000\div50000}=\frac{3}{1}=3:1\)
(b) \(\because\) Money spend by Seema = Earned money - Saved money
= Rs.(150000 - 50000) = Rs.100000
\(\therefore\ Required\ ratio=\frac{Money\ saved\ by\ Seema}{Money\ spend\ by\ Seema}=Rs.\frac{50000}{100000}\)
\(=\frac{50000\div50000}{100000\div50000}=\frac{1}{2}=1:2\) [\(\because\) HCF of 50000 and 100000 = 50000]

Given, total number of students in a class = 30
Number of students who like football = 6
Number of students wholike cricket = 12
Then, number of students who like tennis
= Total number of students - (Number of students who like football + Number of students who like cricket)
= 30 - (6 + 12) = 30 -18 = 12
(a) Ratio of number of students liking football to number of students liking tennis \(=\frac{Number\ of\ students\ who\ like\ football}{Number\ of\ students\ who\ like\ tennis}\)
\(=\frac{6}{12}=\frac{6\div6}{12\div6}=\frac{1}{2}=1:2\) [ \(\because\)HCF of 6 and 12 = 6]
(b) Ratio of number of students liking cricket to total number of students \(=\frac{Number\ of\ students\ who\ like\ cricket}{Total\ number\ of\ students}=\frac{12}{30}\)
\(=\frac{12\div6}{30\div6}=\frac{2}{5}\) [\(\because\)HCF of 12 and 30 = 6]