Maths 3 Mark Question

Largest five-digit number = 99999
Largest three-digit number = 999
By using distributive law, we have:
Product = 99999 × 999
= 99999 × (1000 - 1) [By using distributive law]
= 99999 × 1000 - 99999 × 1
= 99999000 - 99999
= 99899001
Alternate Answer
999 × 99999
= 999 × (100000 - 1) [By using distributive law]
= 999 × 100000 - 999 × 1
= 99900000 - 999
= 99899001

Least 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.

Cost 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.

Cost of a chair = Rs. 1065
Cost of a blackboard = Rs. 1645
Cost of 50 chairs = 50 × 1065 = Rs. 53250
Cost of 30 blackboards = 30 × 1645 = Rs. 49350
Therefore, Total amount of the bill = cost of 50 chairs + cost of 30 blackboards
= Rs (53250 + 49350)
= Rs. 1,02,600

Smallest seven digit number = 1000000
Largest four digit number = 9999
Therefore, Their difference = 1000000 - 9999
= 1000000 - 10000 + 1
= 1000001 - 10000
= 990001

Dividend = 39039, Divisor = 1001, Quotient = 39, Remainder = 0
Check: Divisor × Quotient + Remainder = 1001 × 39 + 0
= 39039
= Dividend
Hence, Dividend = Divisor × Quotient + Remainder
Verified.

Dividend = 34419, Divisor = 149, Quotient = 231, Remainder = 0
Check: Divisor × Quotient + Remainder = 149 × 231 + 0
= 34419
= Dividend
Hence, Dividend = Divisor × Quotient + Remainder
Verified.

Money withdrawn by Mrs.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Now, money left = Money withdrawn - money spent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.

Here, Dividend = 55390, Divisor = 299 and Remainder = 75We have to find the quotient.
Now, Dividend = Divisor × Quotient + Remainder
⇒ 55390 = 299 × Quotient + 75
⇒ 55390 - 75 = 299 × Quotient
⇒ 55315 = 299 × Quotient
⇒ Quotient = 55315 ÷ 299

Hence, quotient = 185

Largest three digit number = 999
Largest five digit number = 99999
Therefore, Product of two numbers = 999 × 99999
= 999 × (100000 - 1)
= 99900000 - 999
= 99899001

Population 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.

Dividend = 612846, Divisor = 582, Quotient = 1053, Remainder = 0
Check: Divisor × Quotient + Remainder = 582 × 1053 + 0
= 612846
= Dividend
Hence, Dividend = Divisor × Quotient + Remainder
Verified.

Uniform speed of a car = 75 km/ h
Distance = Speed × time
= 75 × 98
= 75 × (100 - 2)
= 75 × 100 - 75 × 2
= 7500 - 150
= 7350km
Therefore, The distance covered in 98h is 7350km.

Dividend = 1936, Divisor = 36, Quotient = 53, Remainder = 28
Check: Divisor × Quotient + Remainder = 36 × 53 + 28
= 1936
= Dividend
Hence, Dividend = Divisor × Quotient + Remainder
Verified.

We 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.

Money 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.

Cost of 1 VCR set = Rs. 24350
Cost of 139 VCR sets = 139 × 24350
= 24350 × (140 - 1)
= 24350 × 140 - 24350 × 1
= 3409000 - 24350
= Rs. 3384650
Therefore, The cost of all the VCR sets is Rs. 33,84,650

Dividend = 59761, quotient = 189, remainder = 37 and divisor = ?Dividend = divisor × quotient + remainder
⇒ 59761 = divisor × 189 + 37
⇒ 59761 - 37 = divisor × 189
⇒ 59724 = divisor × 189
⇒ Divisor = 59724 ​÷ 189

Hence, divisor = 316

Dividend = 19881, Divisor = 47, Quotient = 423, Remainder = 0
Check: Divisor × Quotient + Remainder = 47 × 423 + 0
= 19881
= Dividend
Hence, Dividend = Divisor × Quotient + Remainder
Verified.

Dividend = 257796, Divisor = 341, Quotient = 756, Remainder = 0
Check: Divisor × Quotient + Remainder = 341 × 756 + 0
= 257796
= Dividend
Hence, Dividend = Divisor × Quotient + Remainder
Verified.

Cost of construction of 1 house = Rs. 450000
Cost of construction of 197 such houses = 197 × 450000
= 450000 × (200 - 3)
= 450000 × 200 - 450000 × 3
= 90000000 - 1350000
= 88650000
= Therefore, the total cost of construction of 197 houses is Rs. 8,86,50,000