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• What about you? Do you also find Maths difficult?

• What is the most difficult thing in your Maths books? ________

• What do you think is the easiest lesson? ________

**Solution:**

**Disclaimer**: The answer may vary from student to student based on his/her experience. It is highly recommended that the students prepare the answers on their own.

**Find out: how much for a cup of tea?**

Ask people and find out the cost of a cup of tea

• at a tea stall ____________

• at a hotel _______________

**Solution:**

**Disclaimer**: The purpose of this section is to make the students observe their surroundings. The answer may vary from student to student based on his/her experience. It is highly recommended that the students prepare the answers on their own.

If a person who runs a tea stall earns Rs 30 in a day, how much will he earn in 10 days? _____________

And in a month? _______________

How did you get the answer? Discuss.

**Solution:**

Earning of the man in 1 day = Rs 30

Earning of the man in 10 days = Rs 30 × 10

= Rs 300

We do it in the following manner:

1 times 30 is 30.

10 times 30 is 300.

Suppose there are 30 days in a month.

Earning of the man in a month or 30 days = Rs 30 × 30

= Rs 900

We do it in the following manner:

3 times 30 is 90.

30 times 30 is 900.

Hariya and Babu want to buy a handcart for Rs 300.

Who has to pay back more — Hariya or Babu? _____________

**Solution:**

Hariya took a loan of Rs 300 from a bank for 6 months to buy a handcart. He pays

Rs 51 every month to the bank.

Money paid back by Hariya to the bank in 1 month = Rs 51

Money paid back by Hariya to the bank in 6 months = Rs 51 × 6

= Rs 306

We do it in the following manner:

6 $\times $ 50 = 300

6 $\times $ 1 = 6

So,

$\begin{array}{cccc}& 3& 0& 0\\ +& & & 6\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{cccc}& 3& 0& 6\end{array}}}$

So, Hariya paid Rs 306 to the bank after 6 months.

Babu took a loan of Rs 300 from Chunnilal for 6 months to buy a handcart. He paid

Rs 360 to Chunnilal after 6 months.

Thus, Babu has to pay back more than Hariya for buying the handcart.

I have 9 rickshaws of my own. I give the rickshaws on rent. each for Rs 20 a day. On Sundays I do not take any money for them.

• In a week how much does Kiran earn from one rickshaw?

**Solution:**

We know that there are 7 days in a week.

Earning of Kiran from 1 rickshaw per day = Rs 20

Earning of Kiran from 1 rickshaw for 7 days = Rs 20 × 7

= Rs 140

We do it in the following manner:

2 times 7 is 14.

20 times 7 is 140.

Now,

On Sunday, Kiran does not take any money for the rickshaws.

Therefore, earning of Kiran from 1 rickshaw for 6 days = Rs 140 − Rs 20

= Rs 120

We do it in the following manner:

$\begin{array}{ccc}1& 4& 0\\ -& 2& 0\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{\begin{array}{ccc}1& 2& 0\end{array}}}$

So, Kiran will earn Rs 120 in a week from 1 rickshaw.

*Do it mentally and write the answers*.

- 2 × 6 = __________
- 20 × 6 = __________
- 2 × 60 = __________
- 3 × 42 = __________
- 4 × 80 = __________
- 4 × 81 = __________
- 9 × 25 = __________
- 31 × 9 = __________

**Solution:**

- 12
- 120

2 times 6 is 12.

20 times 6 is 120.

- 120
- 126

3 $\times $ 40 = 120

Also, 3 $\times $ 2 = 6

So,

$\begin{array}{ccc}1& 2& 0\\ +& & 6\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{\begin{array}{ccc}1& 2& 6\end{array}}}$

- 320

4 times 8 is 32.

4 times 80 is 320.

- 324

4 $\times $ 80 = 320

Also, 4 $\times $ 1 = 4

So,

$\begin{array}{ccc}3& 2& 0\\ +& & 4\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{\begin{array}{ccc}3& 2& 4\end{array}}}$

- 225

9 $\times $ 20 = 180

Also, 9 $\times $ 5 = 45

So,

$\begin{array}{ccc}& & \\ \stackrel{1}{1}& 8& 0\\ +& 4& 5\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{\begin{array}{ccc}2& 2& 5\end{array}}}$

- 279

30 $\times $ 9 = 270

Also, 1 $\times $ 9 = 9

So,

$\begin{array}{ccc}& & \\ 2& 7& 0\\ +& 0& 9\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{\begin{array}{ccc}2& 7& 9\end{array}}}$

Look up the rate list to see today's rates. Help Kiran to find out the cost of the junk.

• How much will Kiran pay for 31 kg newspaper?

1 kg newspaper costs Rs 5. 30 kg cost Rs 5 × 30 = Rs 150. So for 31 kg she pays Rs _____.

• How much will Kiran pay for 42 kg newspaper?

• Also find the cost of:

(a) 22 kg of plastic

(b) 23 kg of waste paper

(c) 12 kg of iron

Rate-List | |

Kind of Junk | Price of 1 Kg |

1. Waste Paper | Rs 4/- |

2. Newspaper | Rs 5/- |

3. Iron | Rs 12/- |

4. Brass | Rs 170/- |

5. Plastic | Rs 10/- |

Can you do this without writing?

Guess the total money Kiran will pay to the junk collectors. Will it be

— More than 600?

— Less than 600?

**Solution:**

- Cost of 1 kg newspaper = Rs 5

= Rs 155

We do it in the following manner:

5 × 30 = 150

5 × 1 = 5

So,

$\begin{array}{ccc}1& 5& 0\\ +& & 5\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{ccc}1& 5& 5\end{array}}}$

- Cost of 42 kg newspaper = Rs 5 × 42

We do it like this:

5 × 40 = 200

5 × 2 = 10

So,

$\begin{array}{ccc}2& 0& 0\\ +& 1& 0\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{ccc}2& 1& 0\end{array}}}$

(a)

Cost of 1 kg plastic = Rs 10

Cost of 22 kg plastic = 22 × Rs 10

= Rs 220

We do it in the following manner:

22 × 1 = 22

22 × 10 = 220

(b)

Cost of 1 kg waste paper = Rs 4

Cost of 23 kg wastepaper = Rs 4 × 23

= Rs 92

We do it in the following manner:

4 × 20 = 80

4 × 3 = 12

So,

$\begin{array}{ccc}& 8& 0\\ +& 1& 2\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{ccc}& 9& 2\end{array}}}$

(c)

Cost of 1 kg iron = Rs 12

Cost of 12 kg iron = Rs 12 × 12

= Rs 144

We do it in the following manner:

Add the numbers in the box

$\begin{array}{ccc}1& 0& 0\\ & 2& 0\\ & 2& 0\\ +& & 4\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{ccc}1& 4& 4\end{array}}}$

Total money paid to junk collectors will be = Rs 155 + Rs 210 + Rs 220 + Rs 92 + Rs 144

= Rs 821

$\begin{array}{cccc}& & & \\ & \stackrel{2}{1}& \stackrel{1}{5}& 5\\ & 2& 1& 0\\ & 2& 2& 0\\ & & 9& 2\\ +& 1& 4& 4\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{cccc}& 8& 2& 1\end{array}}}$

So, the total money paid to the junk seller is more than Rs 600.

• Kiran bought 1 kg plastic for Rs 10, but sold 1 kg plastic for Rs 12. How much money does she earn on selling 1 kg plastic? Rs _______

So, how much money does she earn for 63 kg? Rs _______

**Solution:**

Cost price of 1 kg plastic = Rs 10

Selling price of 1 kg plastic = Rs 12

Profit on selling 1 kg plastic = Rs (12 − 10)

= Rs 2

Profit on selling 63 kg plastic = Rs 2 × 63

= Rs 126

We do it in the following manner:

2 × 60 = 120

2 × 3 = 6

$\begin{array}{ccc}1& 2& 0\\ +& & 6\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{ccc}1& 2& 6\end{array}}}$

Hence, Kiran will earn Rs 126 on selling 63 kg plastic.

• How much money will Dinu pay for 32 kg iron?

• Kiran buys 1 kg iron for Rs 12 but sells it for Rs 14.

How much does she earn when she sells 32 kg iron? Rs _______

**Solution:**

• Cost of 1 kg iron = Rs 14

Cost of 32 kg iron = Rs 14 × 32

= Rs 448

We do it like this:

Add the numbers in the box

$\begin{array}{cccc}& 3& 0& 0\\ & 1& 2& 0\\ & & 2& 0\\ +& & & 8\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{cccc}& 4& 4& 8\end{array}}}$

So, Dinu will have to pay Rs 448 for 32 kg iron.

- Cost of 1 kg iron for Kiran = Rs 12

Profit on selling 1 kg iron = Rs (14 − 12)

= Rs 2

Profit on selling of 32 kg iron = Rs 2 × 32

= Rs 64

We do it in the following manner:

2 × 30 = 60

2 × 2 = 4

So,

$\begin{array}{cc}6& 0\\ +& 4\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{cc}6& 4\end{array}}}$

Thus, Kiran earns Rs 64 on selling 32 kg iron.

I bought 1 kg newspaper for Rs 5, but sold it for Rs 6. How much money did I earn by selling 152 kg of newspaper? ________

**Solution:**

Cost of 1 kg newspaper = Rs 5

Selling price of 1 kg newspaper = Rs 6

Profit on selling 1 kg newspaper = Rs (6 − 5)

= Re 1

Profit on selling 152 kg newspaper = Re 1 × 152

= Rs 152

I earned Rs 152 on selling 152 kg of newspaper.

How much money will Dinu pay for 4 kg brass? _________

Guess the answer first.

**Solution:**

Cost of 1 kg brass = Rs 180

Cost of 4 kg brass = Rs 4×180

= Rs 720

We will do it as follows:

Add the numbers in the box

$\begin{array}{cccc}& 4& 0& 0\\ +& 3& 2& 0\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{cccc}& 7& 2& 0\end{array}}}$

Thus, Dinu will pay Rs 720 for 4 kg brass.

**First guess the answer and then calculate:**

(a) 37 × 18 =

(b) 45 × 24 =

(c) 69 × 52 =

(d) 77 × 55 =

(e) 142 × 5 =

(f) 382 × 3 =

(g) 2 × 175 =

(h) 4 × 206 =

**Solution:**

(a)

Add the numbers in the box

$\begin{array}{cccc}& 3& 0& 0\\ & 2& 4& 0\\ & & 7& 0\\ +& & 5& 6\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{cccc}& 6& 6& 6\end{array}}}$

(b)

Add the numbers in the box

$\begin{array}{cccc}& & & \end{array}\phantom{\rule{0ex}{0ex}}\begin{array}{cccc}& 8& 0& 0\\ & 1& 0& 0\\ & 1& 6& 0\\ +& & 2& 0\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{cccc}1& 0& 8& 0\end{array}}}$

(c)

Add the numbers in the box

$\begin{array}{cccc}& & & \end{array}\phantom{\rule{0ex}{0ex}}\begin{array}{cccc}3& 0& 0& 0\\ & 4& 5& 0\\ & 1& 2& 0\\ +& & 1& 8\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{cccc}3& 5& 8& 8\end{array}}}$

(d)

Add the numbers in the box

$\begin{array}{cccc}& & & \end{array}\phantom{\rule{0ex}{0ex}}\begin{array}{cccc}\stackrel{1}{3}& \stackrel{1}{5}& 0& 0\\ & 3& 5& 0\\ & 3& 5& 0\\ +& & 3& 5\\ 4& 2& 3& 5\\ & & & \\ & & & \end{array}\phantom{\rule{0ex}{0ex}}$

(e)

Add the numbers in the box

$\begin{array}{cccc}& 5& 0& 0\\ & 2& 0& 0\\ +& & 1& 0\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{cccc}& 7& 1& 0\end{array}}}$

(f)

Add the numbers in the box

$\begin{array}{cccc}& & & \end{array}\phantom{\rule{0ex}{0ex}}\begin{array}{cccc}& 9& 0& 0\\ & 2& 4& 0\\ +& & & 6\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{cccc}1& 1& 4& 6\end{array}}}$

(g).

Add the numbers in the box

$\begin{array}{cccc}& 2& 0& 0\\ & 1& 4& 0\\ +& & 1& 0\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{cccc}& 3& 5& 0\end{array}}}$

(h)

$\begin{array}{cccc}& 8& 0& 0\\ +& & 2& 4\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{cccc}& 8& 2& 4\end{array}}}$

Later she paid Rs 919 to the junk collectors. When she sold the junk she got these notes and coins from Dinu.

Now you make a record in her diary.

Find out how much she earned this time.

**Solution:**

We do it as follows:

5 notes of 100 rupee

5 $\times $ 100 = Rs 500

1 note of 50 rupee

1 $\times $ 50 = Rs 50

18 notes of 10 rupee

18 $\times $ 1 = 18

18 $\times $ 10 = Rs 180

9 notes of 20 rupee

9 $\times $ 2 = 18

9 $\times $ 20 = Rs 180

28 coins of 5 rupee

20 $\times $ 5 = 100

8 $\times $ 5 = 40

$\begin{array}{ccc}1& 0& 0\\ +& 4& 0\end{array}\phantom{\rule{0ex}{0ex}}\overline{)\overline{)\begin{array}{ccc}1& 4& 0\end{array}}}$

28 $\times $ 5 = Rs 140

Money I got = Rs 500 + Rs 50 + Rs 180 + Rs 180 + Rs 140

= Rs 1050

$\begin{array}{cccc}& & & \\ & \stackrel{2}{5}& 0& 0\\ & & 5& 0\\ & 1& 8& 0\\ & 1& 8& 0\\ +& 1& 4& 0\\ 1& 0& 5& 0\\ & & & \end{array}\phantom{\rule{0ex}{0ex}}$

Money I earned = Rs 1050 − Rs 919

= Rs 131

$\begin{array}{ccccc}& {}^{0}\overline{)1}& {}^{1}0& {}^{4}\overline{)5}& {}^{1}0\\ -& & 9& 1& 9\\ & 0& 1& 3& 1\\ & & & & \\ & & & & \end{array}$