NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System

Problems and Solutions

Given below are two columns – Column I and Column II. Match each item of Column I with the corresponding item of Column II.

Arrange the numbers in descending order: 8435, 4835, 13584, 5348, 25843

Of the following numbers which is the greatest? Which is the smallest? 38051425, 30040700, 67205602

Write in expanded form:

(a) 74836

(b) 574021

(c) 8907010

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

(a) Maharashtra: 96878627

(b) Andhra Pradesh: 76210007

(c) Bihar: 82998509

(d) Uttar Pradesh: 166197921

The diameter of Jupiter is 142800000 metres. Write it with commas suitably according to International System of Numeration.

India’s population increased from 439 million in 1961 to 1028 million in 2001. Find total increase and write in Indian System with commas.

Radius of Earth = 6400 km, Radius of Mars = 4300 km. Whose radius is bigger and by how much?

In 2001, populations of Tripura = 3,199,203 and Meghalaya = 2,318,822. Write in words.

In a city, polio drops were given to 2,12,583 children in March 2008 and to 2,16,813 children in April. Find the difference.

A person had Rs 10,00,000. He purchased TV = 16580, Motorcycle = 45890, Flat = 870000. How much money left?

Out of 1,80,000 Vitamin A tablets, 18,734 distributed. Find remaining.

Chinmay had Rs 6,10,000. He gave Rs 87,500 to Jyoti, Rs 1,26,380 to Javed and Rs 3,50,000 to John. How much money left?

Find the difference between the largest 7-digit number and the smallest 8-digit number.

Mobile number: first 4 digits = 9, 9, 8, 7; last 3 digits = 3, 5, 5. Find remaining distinct digits to make greatest possible number.

Mobile number: first 4 digits = 9,9,7,9. Make smallest number using one digit twice from 8,3,5,6,0.

Five-digit number: Ten’s place digit = 4, Unit digit = 1/4 of ten’s place = 1, Hundred’s = 0, Thousand’s = 5×unit = 5, Ten-thousand’s = 2×ten’s = 8. Write number.

Find sum of greatest and least 6-digit numbers formed by digits 2,0,4,7,6,5 (using each digit once).

A container has 35874 litres cold drink. How many bottles of 200 ml each?

Population of a town = 450772. One out of 14 illiterate. Find number of illiterate persons.

Find LCM of 80, 96, 125, 160.

Make greatest and smallest 5-digit numbers using different digits, with 5 at ten’s place.

How many grams should be added to 2kg 300g to make it 5kg 68g?

A box contains 50 biscuit packets each 120g. How many such boxes can be loaded in a van of 900kg?

How many lakhs make 5 billion?

How many millions make 3 crores?

Estimate each of the following by rounding off each number to nearest hundreds:

(a) 874 + 478

(b) 793 + 397

(c) 11244 + 3507

(d) 17677 + 13589

Estimate each of the following by rounding off each number to nearest tens:

(a) 11963 – 9369

(b) 76877 – 7783

(c) 10732 – 4354

(d) 78203 – 16407

Estimate each of the following products by rounding off each number to nearest tens:

(a) 87 × 32

(b) 311 × 113

(c) 3239 × 28

(d) 1385 × 789

The population of a town was 78787 in 1991 and 95833 in 2001. Estimate the increase in population by rounding off each population to nearest hundreds.

Estimate the product \(758 \times 6784\) using the general rule.

A garment factory produced 216315 shirts, 182736 trousers and 58704 jackets in a year. Find the total production.

Find the LCM of \(160, 170\) and \(90\).

A vessel has 13 litres 200 mL of juice. In how many glasses of capacity 60 mL can it be filled?

Determine the sum of the following: (a) successor of 32, (b) predecessor of 49, (c) predecessor of the predecessor of 56, (d) successor of the successor of 67.

A tempo carries 482 boxes of 15 kg each and a van carries 518 boxes of the same weight. Find the total weight.

Leela spent Rs 216766, Rs 122322, Rs 88234 and Rs 26780 on various items. Find the total amount spent.

A box has 5 strips, each with 12 capsules of 500 mg medicine. Find the total weight of medicine in grams in 32 such boxes.

Find the least number that leaves remainder 2 when divided by 3, 4 and 5.

Oil volumes are 120 L, 180 L and 240 L. He fills equal-capacity tins to use all oil. What is the greatest capacity of a tin?

Find a 4-digit odd number using digits 1, 2, 4 and 5 once each such that interchanging the first and last digits gives a number divisible by 4.

Using digits 1, 2, 3 and 4 only once, determine the smallest 4-digit number divisible by 4.

Postal charges are Rs 20, Rs 28 and Rs 36. If stamps of one denomination are to be used, what is the greatest denomination needed?

Biscuit packets contain 12, 15 and 21 biscuits. Find the minimum number of packets of each brand to buy an equal number of biscuits of each brand.

A room is 8 m 96 cm by 6 m 72 cm. Find the minimum number of square tiles of the same size needed to cover the floor.

A library has 780 English and 364 Science books. Each shelf must have the same number of books of each subject. What is the minimum number of books on each shelf?

A van stops every 6th block and a bus every 10th block in a colony of 1 to 100. At which block numbers will both stop?

Test divisibility by 11: (a) 5335 (b) 9020814

Using divisibility tests, determine which of the following are divisible by 4: (a) 4096 (b) 21084 (c) 31795012

Using divisibility tests, which of the following are divisible by 9? (a) 672 (b) 5652