**Ex $1.6$
Miscellaneous Practice Problems
Question $1 .$**

Try to open my locked suitcase which has the biggest 5 digits odd number as the password comprising the digits $7,5,4,3$ and 8 . Find the password.

Solution:

Using a place value chart

The number should be the biggest odd

The password is 87543

**Question 2 .**

As per the census of 2001, the population of four states are given below. Arrange the states in ascending and descending order of their population.

Solution:

All the four values have 8 digits

Comparing the leftmost digits we have $91276115,72626809,72147030,68548437$

Descending order: $91276115>72626809>72147030>68548437$

Ascending order: $68548437<72147030<72626809<91276115$

Ascending order: Rajasthan $<$ Tamil Nadu $<$ Madhy Pradesh $<$ West Bengal

Descending order: West Bengal $>$ Madhya Pradesh $>$ TamilNadu $>$ Rajasthan

**Question $3 .$**

Study the following table and answer the questions.

(i) How many tigers were there in 2011 ?

(ii) How many tigers were less in 2008 than in 1990 ?

(iii) Did the number of tigers increase or decrease between 2011 and 2014 ? If yes, by how much?

Solution:

(i) There are 1706 tigers in 2011

(ii) No. of tigers in $2008=1400$

No. of tigers in $1990=3500$

There were 2100 lesser tigers

(iii) No. of tigers in $2014=2226$

No. of tigers in $2011=1706$

Difference $=520$

$2226>1706$

The number of tigers increased from 2011 to 2014 .

Yes, the number of tigers increased, 520 more tigers are there in $2014 .$

**Question $4 .$**

Mullaikodi has 25 bags of apples. In each bag there are 9 apples. She shares them equally amongst her 6 friends. How many apples do each get? Are there any apples left over?

Solution:

No of apple bags $=25$

Apples in each bag $=9$

Total no of apples $=25 \times 9=225$

Apples shared among her 6 friends $=225 \div 6$

So, among her 6 friends, each of them get 37 apples and 3 apples are left over.

**Question $5 .$**

A Poultry has produced 15472 eggs and fits 30 eggs in a tray. How many trays do they need?

Solution:

Total eggs $=15472$

No. of eggs in 1 tray $=30$

No. of trays needed $=15472 \div 30=516$

No. of trays needed $=516[515+1$ for remaining 22 eggs $]$

**Challenging Problems (Text book Page No.36 \& 37)
Question $6 .$**

Read the table and answer the following questions.

Solution:

(i) Write the Canopus star's diameter in words in the Indian and the International System.

(ii) Write the sum of the place values of 5 in Sirius star's diameter in Indian System.

(iii) Eight hundred sixty-four million seven hundred thirty. Write in Indian System

(iv) Write the diameter in words of Arcturus star in the International System.

(v) Write the difference of the diameters of Canopus and Arcturus star in the Indian and the International Systems.

Solution:

(i) Canopus star's diameter is 25941900 miles

Indian System: Two crores Fifty-Nine Lakh Forty-one thousand Nine Hundred

International System: Twenty-Five Million Nine Hundred Forty-One Thousand Nine Hundred.

(ii) Sirus star's diameter $=1556500 \mathrm{miles}$

Sum of place values of 5 is $5 \times 100000+5 \times 10000+5 \times 100$

$=500000+50000+500$

$=5,50,500$

(iii) Given value is $864,000,730$

In Indian System $86,40,00,730$

Eighty-six crore forty lakhs seven hundred and thirty.

(iv) The diameter of the Arcturus Star is $19,888,800$ miles

Nineteen Million Eight Hundred and Eighty-Eight Thousand Eight Hundred.

(v) The diameter of Canopus $=25941900$

Diameter of Arcturus $=19888800$

Difference $=6053100$

In Indian System $60,53,100$

Sixty lakh fifty-three thousand one hundred.

In International System $6,053,100$

Six Million fifty-three thousand one hundred.

**Question $7 .$**

Anbu asks Arivu Selvi to guess a five digit odd number. He gives the following hints.

i. The digit in the 1000 s place is less than 5

ii. The digit in the 100 s place is greater than 6

iii. The digit in the 10 s place is 8

What is Arivu Selvi answer? Does she give more than one answer?

Solution:

63785,53781

**Question $8 .$**

A Music concert is taking place in a stadium, A total of 7,689 chairs are to be put in rows of $90 .$

(i) How many rows will there be?

(ii) Will there be any chairs left over?

Solution:

(i) There will be 85 rows

(ii) Yes, there are 39 chairs left over.

**Question $9 .$**

Round off the seven-digit number $29,75,842$ to the nearest lakhs and ten lakhs. Are they the same?

Solution:

To the nearest lakhs $=30,00,000$

To the nearest ten lakhs $=30,00,000$

Yes, they are the same.

**Question $10 .$**

Find the 5 or 6 or 7 digit numbers from a newspaper or a magazine to get a rounded number to the nearest ten thousand.

Solution:

(i) $14276 \simeq 10000$

(ii) $1,86945 \simeq 1,90000$