Question 13 Marks
Find the product of the largest $5-$digit number and the largest $3-$digit number using distributive law.
AnswerLargest five-digit number $= 99999$
Largest three-digit number $= 999$ By using distributive law,
we have: Product $= 99999 \times 999 = 99999 \times (1000 - 1)$
[By using distributive law] $= 99999 \times 1000 - 99999 \times 1 = 99999000 - 99999 = 99899001$
Alternate Answer
$999 \times 99999 = 999 \times (100000 - 1)$
[By using distributive law] $= 999 \times 100000 - 999 \times 1 = 99900000 - 999 = 99899001$
View full question & answer→Question 23 Marks
Divide, and find out the quotient and remainder. Check your answer.
$4178 ÷ 35$
Answer
Dividend $= 119$ and Remainder $= 13$
Check: Divisor $\times $ Quotient $+$ remainder $= 35 \times 119 + 13 $
$= 4178$
= Dividend
$\therefore$ Dividend $=$ Divisor $\times $ Quotient $+$ Remainder
Verified. View full question & answer→Question 33 Marks
Find the least 6-digit number exactly divisible by $83.$
AnswerLeast six-digit number $= 100000$ Here, dividend $= 100000$ and divisor $= 83$
In order to find the least $6-$digit number exactly divisible by $83,$
we have to add $83 - 68 = 15$ to the dividend.
I.e., $100000 + 15 = 100015$
So, $100015$ is the least six-digit number exactly divisible by $83.$ View full question & answer→Question 43 Marks
1 dozen bananas cost $Rs. 29$. How many dozens can be purchased for $Rs. 1392?$
AnswerCost of $1$ dozen bananas $= Rs. 29$
Number of dozens purchased for $Rs. 1392 = 1392 ÷ 29$
Hence, $48$ dozen of bananas can be purchased with $Rs. 1392.$ View full question & answer→Question 53 Marks
$50$ chairs and $30$ blackboards were purchased for a school. If each chair costs $Rs. 1065$ and each blackboard cost $Rs. 1645$, find the total amount of the bill.
AnswerCost of a chair $= Rs. 1065$
Cost of a blackboard $= Rs. 1645$
Cost of 50 chairs$ = 50 \times 1065 = Rs. 53250$
Cost of 30 blackboards$ = 30 \times 1645 = Rs. 49350$
Therefore, Total amount of the bill $=$ cost of $50$ chairs $+$ cost of $30$ blackboards
$= Rs (53250 + 49350)$
$= Rs. 1,02,600$
View full question & answer→Question 63 Marks
Find the difference between the smallest number of $7$ digits and the largest number of $4$ digits.
AnswerSmallest seven digit number $= 1000000$
Largest four digit number $= 9999$
Therefore, Their difference $= 1000000 - 9999 $
$= 1000000 - 10000 + 1$
$ = 1000001 - 10000 $
$= 990001$
View full question & answer→Question 73 Marks
Divide and check your answer by the corresponding multiplication in the following:
$39039 ÷ 1001$
Answer
Dividend $= 39039,$
Divisor $= 1001,$
Quotient $= 39,$
Remainder $= 0$
Check: Divisor $\times $ Quotient $+$ Remainder $= 1001 \times 39 + 0$
$= 39039$
$=$ Dividend
Hence, Dividend = Divisor $\times$ Quotient + Remainder
Verified. View full question & answer→Question 83 Marks
Divide and check your answer by the corresponding multiplication in the following:
$34419 ÷ 149$
Answer
Dividend $= 34419,$
Divisor $= 149,$
Quotient $= 231,$
Remainder $= 0$
Check: Divisor $\times $ Quotient $+$ Remainder $= 149 \times 231 + 0$
$= 34419$
$=$ Dividend
Hence, Dividend $=$ Divisor $\times $ Quotient $+$ Remainder
Verified. View full question & answer→Question 93 Marks
Divide, and find out the quotient and remainder. Check your answer. $23025 ÷ 1000$
Answer
Quotient $= 23$ and remainder $= 25$
Check: Divisor $\times $ Quotient $+$ Remainder $=1000 \times 23 + 25 = 23025 =$ Dividend
$\therefore$ Dividend $=$ Divisor $\times $ Quotient $+$ Remainder Verified. View full question & answer→Question 103 Marks
Divide, and find out the quotient and remainder. Check your answer. $93575 ÷ 400$
Answer
Quotient $= 233$ and Remainder $= 375$
Check: Divisor $\times $ Quotient $+$ Remainder $= 400 \times 233 + 375 = 93575 =$ Dividend
$\therefore$ Dividend $=$ Divisor $\times $ Quotient $+$ Remainder Verified. View full question & answer→Question 113 Marks
Mrs. Saxena withdrew $Rs. 100000$ from her bank account. She purchased a $TV$ set for $Rs. 38750,$ a refrigerator for $Rs. 23890$ and jewelry worth $Rs. 35560$. How much money was left with her?
AnswerMoney withdrawn by Mrs. Saxena $= Rs. 1,00,000$
Cost of the $TV$ set $= Rs. 38,750$
Cost of the refrigerator $= Rs. 23,890$
Cost of the jewellery $= Rs. 35,560$
Total money spent $= Rs. (38750 + 23890 + 35560) = Rs. 98200$
Now, money left = Money withdrawn - money spent
$= Rs. (100000 - 98200)$
$= Rs. 1800$
Therefore, $Rs. 1,800 $is left with Mrs. Saxena.
View full question & answer→Question 123 Marks
On dividing $55390$ by $299$, the remainder is $75$. Find the quotient using the division algorithm.
AnswerHere, Dividend $= 55390$, Divisor $= 299$ and Remainder $= 75$
We have to find the quotient.
Now, Dividend = Divisor $\times $ Quotient + Remainder
$\Rightarrow 55390 = 299 \times $ Quotient $+ 75$
$\Rightarrow 55390 - 75 = 299 \times $ Quotient
$\Rightarrow 55315 = 299 \times $ Quotient
$\Rightarrow $ Quotient $= 55315 ÷ 299$
Hence, quotient $= 185$ View full question & answer→Question 133 Marks
Find the product of the largest $3$ digit number and the largest $5$ digit number.
AnswerLargest three digit number $= 999$
Largest five digit number $= 99999$
Therefore, Product of two numbers $= 999 \times 99999$
$= 999 \times (100000 - 1)$
$= 99900000 - 999$
$= 99899001$
View full question & answer→Question 143 Marks
The population of a town was $110500$. In one year it increased by $3608$ due to new births. However, $8973$ persons died or left the town during the year. What was the population at the end of the year?
AnswerPopulation of the town $= 110500$
Increased population $= 110500 + 3608 = 114108$
Number of persons who died or left the town $= 8973$
Population at the end of the year $= 114108 - 8973 = 105135$
Therefore, The population at the end of the year will be $105135.$
View full question & answer→Question 153 Marks
The cost price of $23 TV$ sets is $Rs. 570055$. Find the cost of each such set.
AnswerCost price of $23$ $TV$ sets $= Rs. 5,70,055$
Cost price of $1 TV$ set $= 570055 ÷ 2$
$\therefore$ The cost of one $TV$ set is $Rs. 24,785.$ View full question & answer→Question 163 Marks
Divide and check your answer by the corresponding multiplication in the following: $612846 ÷ 582$
Answer
Dividend $= 612846$, Divisor $= 582,$
Quotient $= 1053$, Remainder $= 0$
Check: Divisor $\times $ Quotient $+$ Remainder $= 582 \times 1053 + 0 = 612846$
$=$ Dividend Hence, Dividend $=$ Divisor $\times $ Quotient $+$ Remainder Verified. View full question & answer→Question 173 Marks
A car moves at a uniform speed of $75 \ km/ h$. How much distance will it cover in $98$ hours?
AnswerUniform speed of a car $= 75 \ km/ h$
Distance $=$ Speed $\times $ time $= 75 \times 98 = 75 \times (100 - 2) = 75 \times 100 - 75 \times 2 = 7500 - 150 = 7350\ km$ Therefore, The distance covered in $98h$ is $7350\ km.$
View full question & answer→Question 183 Marks
The cost price of $23$ colour television sets is $Rs. 570055$. Determine the cost price of each $TV$ set if each costs the same.
AnswerCost price of $23$ colour $TV$ sets $= Rs. 5,70,055$ Cost price of $1 TV$ set $= Rs. 570055 ÷ 23$
$\therefore$ The cost price of one $TV$ set is $Rs 24,785.$ View full question & answer→Question 193 Marks
Divide, and find out the quotient and remainder. Check your answer. $36195 ÷ 153$
Answer
Quotient $= 236$ and
Remainder $= 87$
Check: Divisor $\times $ Quotient $+$ Remainder $= 153 \times 236 + 87 = 36195 =$ Dividend
$\therefore$ Dividend $=$ Divisor $\times $ Quotient $+$ Remainder Verified. View full question & answer→Question 203 Marks
Divide and check your answer by the corresponding multiplication in the following: $1936 ÷ 36$
Answer
Dividend $= 1936$,
Divisor $= 36,$
Quotient $= 53,$
Remainder $= 28$
Check: Divisor $\times $ Quotient $+$ Remainder $= 36 \times 53 + 28 = 1936 =$ Dividend
Hence, Dividend $=$ Divisor $\times $ Quotient $+$ Remainder Verified. View full question & answer→Question 213 Marks
Find the largest $4-$digit number divisible by $16.$
AnswerWe have to find the largest four digit number divisible by $16.$
The largest four-digit number $= 9999$
Therefore, dividend $= 9999$
Divisor $= 16$
Here, we get remainder $= 15$
Therefore, $15$ must be subtracted from 9999 to get the largest four digit number that is divisible by $16.$
i.e., $9999 - 15 = 9984$
Thus, $9984$ is the largest four-digit number that is divisible by $16.$ View full question & answer→Question 223 Marks
Ravi opened his account in a bank by depositing $Rs. 136000$. Next day he withdrew $Rs. 73129$ from it. How much money was left in his account.
AnswerMoney deposited by Ravi $= Rs. 1,36,000$
Money withdrawn by Ravi $= Rs. 73,129$
Money left in his account $=$ Money deposited - Money withdrawn
$= Rs. (136000 - 73129)$
$= Rs. 62871$
Therefore, $Rs. 62,871$ is left in Ravi’s account.
View full question & answer→Question 233 Marks
Find the largest $6-$digit number divisible by $16.$
AnswerLargest six-digit number $= 999999$
Remainder $= 15$ Largest six-digit number divisible by $16 = 999999 - 15 = 999984$
$\therefore 999984$ is divisible by $16.$ View full question & answer→Question 243 Marks
A dealer purchased $139 VCRs$. If the cost of each set is $Rs. 24350$, find the cost of all the sets together.
AnswerCost of $1 VCR$ set $= Rs. 24350$
Cost of $139 VCR$ sets $= 139 \times 24350 = 24350 \times (140 - 1) = 24350 \times 140 - 24350 \times 1 = 3409000 - 24350 = Rs. 3384650$
Therefore, The cost of all the $VCR$ sets is $Rs. 33,84,650$
View full question & answer→Question 253 Marks
The product of two numbers is $504347$. If one of the numbers is $317$, find the other.
AnswerLet $x$ and $y$ be the two numbers.
Product of the two numbers $= x \times y = 504347$
If $x = 317$,
we have: $317 \times y = 504347$
$\Rightarrow y = 504347 ÷ 317$
$y = 1591$
$\therefore$ The other number is $1591.$ View full question & answer→Question 263 Marks
Divide the largest $5$ digit number by $653.$ Check your answer by the division algorithm.
AnswerLargest five-digit number $= 99999$
Dividend $= 99999$,
Divisor $= 653$,
Quotient $= 153$ and
Remainder $= 90$
Check: Divisor $\times $ Quotient $+$ Remainder
$= 653 \times 153 + 90$
$= 99909 + 90$
$= 99999$
= Dividend
$\therefore$ Dividend $=$ Divisor $\times $ Quotient $+$ Remainder
Verified. View full question & answer→Question 273 Marks
19625 trees have been equally planted in $157$ rows. Find the number of trees in each row.
AnswerNumber of trees planted in $157$ rows $= 19625$
Trees planted in $1$ row $= 19625 ÷ 157$
$\therefore 125$ trees are planted in each row. View full question & answer→Question 283 Marks
On dividing $59761$ by a certain number, the quotient is $189$ and the remainder is $37.$ Find the divisor.
View full question & answer→Question 293 Marks
Divide and check your answer by the corresponding multiplication in the following:
$19881 ÷ 47$
Answer
Dividend $= 19881,$
Divisor $= 47$,
Quotient $= 423$,
Remainder $= 0$
Check: Divisor $\times $ Quotient $+$ Remainder $= 47 \times 423 + 0$
$= 19881$
$=$ Dividend
Hence, Dividend $=$ Divisor $\times $ Quotient $+$ Remainder
Verified. View full question & answer→Question 303 Marks
Divide $53968$ by $267$ and check the result by the division algorithm.
Answer
Dividend $= 53968,$
Divisor $= 267,$
Quotient $= 202$ and
Remainder $= 34$ Check: Quotient $\times $ Divisor $+$ Remainder
$= 267 \times 202 + 34 = 53934 + 34 = 53968$
$\therefore$ Dividend $=$ Quotient $\times $ Divisor $+$ Remainder Verified. View full question & answer→Question 313 Marks
Divide and check your answer by the corresponding multiplication in the following: $257796 ÷ 341$
Answer
Dividend $= 257796,$
Divisor $= 341,$
Quotient $= 756,$
Remainder $= 0$
Check: Divisor $\times $ Quotient $+$ Remainder
$= 341 \times 756 + 0 = 257796 $
$=$ Dividend Hence, Dividend
$=$ Divisor $\times $ Quotient $+$ Remainder Verified. View full question & answer→Question 323 Marks
The population of a town is $517530$. If one out of every $15$ is reported to be literate, find how many literate persons are there in the town.
AnswerPopulation of the town $= 517530 (115) 115$ of the population is reported to be literate,
i.e., $(115) 115 × 517530 = 517530 ÷ 15$ 
$\therefore$ There are $34502$ illiterate persons in the given town. View full question & answer→Question 333 Marks
A housing society constructed $187$ houses. If the cost of construction for each house is $Rs. 450000$, what is the total cost for all the houses?
AnswerCost of construction of $1$ house $= Rs. 450000$ Cost of construction of $197$ such houses $= 197 \times 450000 = 450000 \times (200 - 3) = 450000 \times 200 - 450000 \times 3 = 90000000 - 1350000 = 88650000 =$ Therefore, the total cost of construction of $197$ houses is $Rs. 8,86,50,000$
View full question & answer→Question 343 Marks
Divide, and find out the quotient and remainder. Check your answer. $6971 ÷ 47$
Answer
Quotient $= 148$ and
Remainder $= 15$
Check: Divisor $\times $ Quotient $+$ Remainder $= 47 \times 148 + 15 = 6971 =$ Dividend
$\therefore$ Dividend = Divisor $\times $ Quotient $+$ Remainder Verified. View full question & answer→Question 353 Marks
Divide, and find out the quotient and remainder. Check your answer. $16135 ÷ 875$
Answer
Quotient $= 18$ and
Remainder $= 385$
Check: Divisor $\times $ Quotient $+$ Remainder
$= 875 \times 18 + 385 = 16135 =$ Dividend
$\therefore$ Dividend $=$ Divisor $\times $ Quotient $+$ Remainder Verified. View full question & answer→