3 Marks Question

Question 13 Marks

Write $10075302$ in words and rearrange the digits to get the smallest and the largest numbers.

Answer

One crore seventy-five thousand three hundred two:
In order to write the smallest $8$-digit number using digits $0, 1, 2, 3, 5$ and $7$, we put the smallest digit $1$ (Except $0$) at the place having the highest place value.
The largest digit $7$ is put at the rightmost place i.e. at unit’s place, the digit $5$ is put at the ten’s place, the digit $3$ is put at the hundred’s place and the digit $2$ is put at the thousand’s place. All other places are filled by $0$.
Hence, the required largest number is $10002357$.
In order to write the largest $8$-digit number using digits $0, 1, 2, 3, 5$ and $7$, we put the largest digit $7$ at the place having the highest place value.
The smallest digit $5$ is put at the place after the highest place value.
We put the next smallest digit (i.e., $3$) after the previous one.
After it we place the next smallest digit (i.e., $2$) and after that we put the digit $1$. All other places are filled by $0$.
Hence, the required largest number is $75321000.$

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Question 23 Marks

A box of medicine tablets contains $2,00,000$ tablets each weighing $20mg$. what is the total weight of all the tablets in the box in grams? in kilograms?

Answer

Given data :
Each tablet weighs $= 20\ mg$ Therefore,
The weight of $2,00,000$ tablets $= 2,00,000 \times 20 = 40,00,000\ mg$
Therefore, The total weight of all the tablets in the box $= 40,00,000\ mg$ We know $1g = 1,000\ mg$
Weight of the box having all tablets$ = 40,00,000 ÷ 1,000 = 4000g$ And, as $1\ kg = 1,000g$
Therefore, Weight of the box having all tablets $= 4,000 ÷ 1,000 = 4000g = 4\ kg$

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Question 33 Marks

Write the greatest and the smallest numbers of $4$ digits that can be formed using the digits $0, 8, 7, 5$ ; using each digit only once.

Answer

In order to write the largest $4$-digit number using digits $0, 5, 7$ and $8$, we put the largest digit $8$ at the place having the highest place value. The smallest digit $0$ is put at the right most place i.e. at unit's place, the digit $7$ is put at the hundred's place and the digit $5$ is put at the ten's place. Hence, the required largest number is $8750$. In order to write the smalest $4$-digit number using digits $0, 5, 7$ and $8$, we put the smallest digit $5$ (Except $0$) at the place having the highest place value. The largest digit $8$ is put at the right most place i.e. at unit's place, the digit $7$ is put at the ten's place and the digit $0$ is put at the hundred's place. Hence, the required largest number is $5078.$

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Question 43 Marks

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

Answer

As given in the question, Total capacity of a van carrying boxes of medicines $= 800\ kg = 8,00,000g (1\ kg = 1,00g)$
As given in the question, Weight of each packed box $= 4,500g = 4,000 + 500 = 4,500g$
Therefore, Total number of boxes that can be loaded in the van $= \frac{8, 00,000}{4,500} = 177.77$
The obtained number of boxes is not a whole number.
Therefore, Weight of $177$ boxes$ = 177 \times 4,500 = 7,96,500g$ (under permissible limit)
Therefore, Weight of $178$ boxes = $178 \times 4,500 = 8,01,000g$ (beyond permissible limit)
Therefore, we can’t load $178$ boxes; hence, we can say that $177$ boxes can be loaded in the van.

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Question 53 Marks

Estimate the product $475 \times 225$ rounding off each number to the nearest hundred.

Answer

In $475$ the last two digits i.e., $75$ is greater than $50$.
Hence, $1$ will be added to the $3$rd last digit and the last two digits will become zero.
After rounding to nearest hundred we will get $500$. In $225$ the last two digit i.e., $25$ is less than $50.$
Hence, the $3$rd last will remain same and the last digit will become zero.
After rounding to nearest ten we will get $200$. Required product $500 \times 200 = 1,00,000$

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Question 63 Marks

The town newspaper is published every day. One copy has $12$ pages. Everyday $11,980$ copies are printed. How many pages are in all printed every day? Every month?

Answer

As given in the question, Number of pages in $1$ copy of newspaper $= 12$
Therefore, Number of pages in $11,980$ copies of newspaper $= 11, 980 \times 12 = 1,43,760$
Thus, $1,43,760$ pages are printed every day. Now, number of pages printed every day $= 1,43,760$
Therefore, Number of pages printed in a month $= 1,43,760 \times 30 = 43,12,800$
Thus, $43,12,800$ pages are printed in a month.

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Question 73 Marks

Population of sundarnagar was $2,35,471$ in the year $1991$. In the year $2001$ it was found to have increased by $72,958$. What was the population of the city in $2001$?

Answer

The population of Sundar Nagar in $2001 =$ Sum of the population of city in $1991$ + Increase in population over the given time period As given in the question,
The population of Sundar Nagar in $1991 = 2,35,471$
As given in the question, Increase in population over the given time period $= 72.958$
Therefore, The population of Sundar Nagar in $2001 = 2,35,471 + 72,958 = 3,08,429$

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Question 83 Marks

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

Answer

As given in the question, Total length of available cloth $= 40m = 4,000\ cm (1m = 100\ cm)$
As given in the question, Length of cloth required to stitch a shirt $= 215\ cm = 200 + 15 = 215\ cm$
Therefore, The number of shirts that can be stitched from the $40$-metre cloth $= \frac{4,000}{215} = 18.60$
As the number of shirts has to be a whole number, we consider the whole part only.
That is, $18$ such shirts can be stitched. Therefore, Cloth required for stitching $18$ shirts $= 215 × 18 = 3870cm.$
Therefore, Remaining cloth $= 4,000 - 3870 = 130\ cm = 1.3m$

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Question 93 Marks

Write the greatest $6$-digit number formed by three different digits.

Answer

To write the greatest $6$-digit number having three different digits, we will have to use three largest digits.
Clearly $9, 8$ and $7$ are three largest digits.
In order to write the largest $6$-digit number using digits $7, 8$ and $9$,
we put the largest digit $9$ at the place having the highest place value.
The smallest digit $7$ is put at the right most place i.e. at unit's place and the digit $8$ is put at the ten's place.
All other places are filled by $9$. Hence, the required number $= 999987.$

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Question 103 Marks

Write the smallest and the largest six digit numbers. How many numbers are between these two.

Answer

The smallest digit is $0.$ But we cannot use $0$ at the place having the highest place value in six digit numbers.
So, we will use the second smallest digit i.e., $1$. All other places are filled by $9$.
Hence, the required number $= 100000$ Smallest six digit number will be $100000$.
The largest digit is $9$. We can use $9$ at any place. In fact, we can use $9$ in all places in six digit numbers.
Hence, the required number $= 999999$ Largest six digit number will be $999999$
Required difference $= 999999 - 100000 = 899999$
So, the total numbers between $999999$ and $100000$ will be $899998.$

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Question 113 Marks

Ravish has $Rs. 78,592$ with him. He placed an order for purchasing $39$ radio sets at $Rs. 1234$ each. How much money will remain with him after the purchase?

Answer

Ravish’s initial money $= Rs.78,592$ He purchased $39$ radio sets at $Rs.1234$ each.
Therefore, Money spent by him on purchasing $39$ radio sets $= 1,234 \times 39 = Rs. 48,126$
Therefore, Remaining money with Ravish after the purchase = Initial money-Money spent on purchasing $39$ radio sets $= Rs. 78,592 - Rs. 48,126 = Rs. 30,466$
Thus, $230,466$ are left with him after the purchase.

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Question 123 Marks

A vessel has $4$ litre and $650ml$ of curd. In how many glasses, each of $25ml$ capacity, can it be distributed?

Answer

The number of glasses in which curd can be distributed = Total amount of curd/ Capacity of each glass.
Total amount of curd in the vessel $= 4,650ml = 4,000 + 650 = 4,650ml (1L = 1,000ml)$
Capacity of each glass $= 25ml$
Therefore, Number of glasses in which curd can be distributed $= \frac{4,650}{25} = 186$

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Question 133 Marks

In an election, the successful candidate registered $5, 77,570$ votes and his nearest rival secured $3,48,685$ votes. By what margin did the successful candidate win the election?

Answer

Margin of victory in the election for the successful candidate = Number of votes registered by the winner-Number of votes secured by nearest rival candidate
Votes registered by the winner $= 5,77,570$
Votes secured by the rival $= 3,48,685$
Therefore, Margin of victory for the successful candidate
$= 5,77,570 - 3,48,685 = 2,28, 885$

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Question 143 Marks

The Distance between the school and the house of a student is $1Km$ $875m$. Every day she walks both ways between her school and home. Find the total distance covered by her in a week?

Answer

Therefore, Distance between the school and the house of a student $= 1,875m = 1,000 + 875 = 1,875m (1km = 1,000m)$
As given in the question, Distance covered by a student in a day $= 2 \times 1,875 = 3,750m$
Total distance covered by her in a week $= 7 \times 3,750 = 26,250m = 26.25\ km$

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Maths 3 Marks Question

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