Chapter - 1 -EXERCISE 1.2 - Knowing our Numbers Numbers (NCERT Class 6th Maths Solution)

1. A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final day was respectively 1094, 1812, 2050 and 2751. Find the total number of tickets sold on all the four days.

Solution/Explanation:

Tickets sold on $1$st day $=1094$
Tickets sold on $2$nd day $=1812$
Tickets sold on $3$rd day $=2050$
Tickets sold on $4$th day $=2751$
Total tickets sold$=1094+1812+2050+2751$
$1094$
$1812$
$2050$
$+2751$
__________
$7707$
__________
$\therefore$ Total tickets sold $=7,707$.

2. Shekhar is a famous cricket player. He has so far scored 6980 runs in test matches. He wishes to complete 10,000 runs. How many more runs does he need?

Solution/Explanation:

Runs scored so far$=6980$
Runs Shekhar wants to score$=10,000$
More runs required $=10,000-6980$
$10000$
$-6980$
_________
$3020$
_________
$\therefore$ Shekhar requires $3,020$ more runs.

3. In an election, the successful candidate registered 5,77,500 votes and his nearest rival secured 3,48,700 votes. By what margin did the successful candidate win the election?

Solution/Explanation:

successful candidate secured = 5,77,500${\displaystyle 5,77,500}$ votes
rival candidate secured= 3,48,700${\displaystyle 3,48,700}$ votes
winning margin = 577500−348700${\displaystyle 577500-348700}$
=228800${\displaystyle =228800}$ votes 

4. Kirti bookstore sold books worth ` 2,85,891 in the first week of June and books worth ` 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?

Solution/Explanation:

Value of Books sold in $1$st week$=$Rs. $2,85,891$
Value of books sold in $2$nd week$=$Rs. $4,00,768$
Total sale$=$Sale in $1$st week$+$ Sale in $2$nd week$=2,85,891+4,00,768$
 $285891$
$+400768$
___________
$686659$
___________
The sale for the two weeks together was $6,86,659$.
Since $4,00,768>2,85,891$, sale in $2$nd week was greater than $1$st week.
 $400768$
$-285891$
___________
$114877$
___________
$\therefore$ The sale in $2$nd week was longer than the sale in $1$st week by Rs. $1,14,877$.

5. Find the difference between the greatest and the least 5-digit number that can be written using the digits 6, 2, 7, 4, 3 each only once.

Solution/Explanation:

The digits which can be used are 6,2,7,4,3 and can be each used only once.

The greatest number possible=76,432

The least number possible=23,467

Difference between the greatest and smallest number=76,432-23,467

                                                                                       =52,965

Thus, the difference between the greatest and the least number is 52,965.

6. A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?

Solution/Explanation:

Screws produced in one day $=2,825$
Days in January$=31$
Screws produced in $31$ days $=2825\times 31$
$2825$
$\times 31$
____________
$2825$
$+84750$
____________
$87575$
____________
Therefore, screws produced during Jan, $06=87,575$.

7. A merchant had ` 78,592 with her. She placed an order for purchasing 40 radio sets at ` 1200 each. How much money will remain with her after the purchase?

Solution/Explanation:

Cost of one radio set $=$Rs. $1200$
Cost of $40$ radio sets $=1200\times 40$ Rs. $48000$
Money with Merchant$=$Rs. $78,592$
Money spent$=$Rs. $48,000$
Money left $=78592-48000$
$78592$
$-48000$
___________
$30592$
___________
Therefore, Rs. $30,592$ will remain with her after the purchase.

8. A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer? (Hint: Do you need to do both the multiplications?)

Solution/Explanation:

Difference between $65$ and $56=9$
Difference in the answer$=7236\times 9$
$7236$
$\times 9$
_________
$65124$
_________
Therefore, His answer was greater than the correct answer by $65,124$.

9. To stitch a shirt, 2 m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain?

(Hint: convert data in cm.)

Solution/Explanation:

Length of cloth needed for stitching $1$ shirt$=2m15cm$

 $=2m+15cm$

$=2\times 1m+15cm$

$=2\times 100cm+15cm$            (since $1m=100cm$)

Length of cloth needed for stitching $1$ shirt$=200+15=215cm$

Total length of cloth available$=40$m

since $1m=100cm$

Total length of cloth available$=40\times 100$cm 

Total length of cloth available$=4000$cm

Total number of shirts can be made from available cloth

$=\frac{Totallengthofclothavailable}{Lengthofclothneededfor1shirt}$

Total number of shirts can be made from available cloth$=\frac{4000}{215}$

Quotient$=18$ and Remainder$=130$

$\therefore$ number of shirts that can be made$=18$

and remaining cloth$=130cm$

                                  $=100cm+30cm$

since $1m=100cm$

Remaining cloth$=1m30cm$ 

10. Medicine is packed in boxes, each weighing 4 kg 500g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg?

Solution/Explanation:

$1$ kg $=1000$g
$4$ kg $500$ g$=4500$g
$800$ kg $=8\times 1000=800000$g
Number of boxes that can be loaded in the van $=800000÷4500$
            $177$
           _________
$4500)800000$
            $4500$
           _________
            $35000$
            $31500$
           _________
               $35000$
               $31500$
              ___________
                   $3500$
              ___________
Hence, $177$ boxes at maximum can be loaded in the van.

11. The distance between the school and a student’s house is 1 km 875 m. Everyday she walks both ways. Find the total distance covered by her in six days.

 Solution/Explanation:

Distance between school and house$=1$ km $875$ m
Now, $1$ km $=1000$m
Distance covered each day $=1875\times 2=3750$m
Distance covered in $6$ days $=3750\times 6$
$3750$
$\times 6$
___________
$22500$
___________
Therefore, distance covered in $6$ days$=22,500$ m $=22.5$ or $22$ km $500$ m.

12. A vessel has 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?

 Solution/Explanation:

Total curd in vessel =4.5L=4500mL

Capacity of a lass =25mL

∴${\displaystyle \therefore }$ Number of glasses that can be filled with curd =450025=180