NCERT Exemplar Solutions
Class 6 - Mathematics

Unit 7: Algebra

The distance (in km) travelled in h hours at a constant speed of 40 km per hour is _________.

p kg of potatoes are bought for Rs 70. Cost of 1 kg of potatoes (in Rs) is _________.

An auto rickshaw charges Rs 10 for the first kilometre then Rs 8 for each such subsequent kilometre. The total charge (in Rs) for d kilometres is _________.

If 7x + 4 = 25, then the value of x is _________.

The solution of the equation 3x + 7 = –20 is _________.

‘x exceeds y by 7’ can be expressed as _________.

‘8 more than three times the number x’ can be written as _________.

Number of pencils bought for Rs x at the rate of Rs 2 per pencil is _________.

The number of days in w weeks is _________.

Annual salary at r rupees per month along with a festival bonus of Rs 2000 is _________.

The two digit number whose ten’s digit is ‘t’ and units’s digit is ‘u’ is _________.

The variable used in the equation 2p + 8 = 18 is _________.

x metres = _________ centimetres.

p litres = _________ millilitres.

r rupees = _________ paise.

If the present age of Ramandeep is n years, then her age after 7 years will be _________.

If I spend f rupees from 100 rupees, the money left with me is _________ rupees.

0 is a solution of the equation x + 1 = 0

The equations x + 1 = 0 and 2x + 2 = 0 have the same solution.

If m is a whole number, then 2m denotes a multiple of 2.

The additive inverse of an integer x is 2x.

If x is a negative integer, –x is a positive integer.

2x – 5 > 11 is an equation.

In an equation, the LHS is equal to the RHS.

In the equation 7k – 7 = 7, the variable is 7.

a = 3 is a solution of the equation 2a – 1 = 5

The distance between New Delhi and Bhopal is not a variable.

t minutes are equal to 60t seconds.

x = 5 is the solution of the equation 3x + 2 = 20

‘One third of a number added to itself gives 8’, can be expressed as x/3 + 8 = x

The difference between the ages of two sisters Leela and Yamini is a variable.

The number of lines that can be drawn through a point is a variable.

One more than twice the number.

20°C less than the present temperature.

The successor of an integer.

The perimeter of an equilateral triangle, if side of the triangle is m.

Area of the rectangle with length k units and breadth n units.

Omar helps his mother 1 hour more than his sister does.

Two consecutive odd integers.

Two consecutive even integers.

Multiple of 5.

The denominator of a fraction is 1 more than its numerator.

The height of Mount Everest is 20 times the height of Empire State building.

If a note book costs Rs p and a pencil costs Rs 3, then the total cost (in Rs) of two note books and one pencil.

z is multiplied by –3 and the result is subtracted from 13.

p is divided by 11 and the result is added to 10.

x times of 3 is added to the smallest natural number.

6 times q is subtracted from the smallest two digit number.

Write two equations for which 2 is the solution.

Write an equation for which 0 is a solution.

Write an equation whose solution is not a whole number.

A pencil costs Rs p and a pen costs Rs 5p.

Leela contributed Rs y towards the Prime Minister’s Relief Fund. Leela is now left with Rs (y + 10000).

Kartik is n years old. His father is 7n years old.

The maximum temperature on a day in Delhi was p°C. The minimum temperature was (p − 10)°C.

John planted t plants last year. His friend Jay planted 2t + 10 plants that year.

Sharad used to take p cups tea a day. After having some health problem, he takes p − 5 cups of tea a day.

The number of students dropping out of school last year was m. Number of students dropping out of school this year is m − 30.

Price of petrol was Rs p per litre last month. Price of petrol now is Rs (p − 5) per litre.

Khader’s monthly salary was Rs P in the year 2005. His salary in 2006 was Rs (P + 1000).

The number of girls enrolled in a school last year was g. The number of girls enrolled this year in the school is 3g − 10.

Translate each of the following statements into an equation, using x as the variable:

(a) 13 subtracted from twice a number gives 3.

(b) One fifth of a number is 5 less than that number.

(c) Two-third of number is 12.

(d) 9 added to twice a number gives 13.

(e) 1 subtracted from one-third of a number gives 1.

Translate each of the following statements into an equation:

(a) The perimeter (p) of an equilateral triangle is three times of its side (a).

(b) The diameter (d) of a circle is twice its radius (r).

(c) The selling price (s) of an item is equal to the sum of the cost price (c) of an item and the profit (p) earned.

(d) Amount (a) is equal to the sum of principal (p) and interest (i).

Let Kanika’s present age be x years. Complete the following table, showing ages of her relatives:

If m is a whole number less than 5, complete the table and by inspection of the table, find the solution of the equation 2m − 5 = −1 :

A class with p students has planned a picnic. Rs 50 per student is collected, out of which Rs 1800 is paid in advance for transport. How much money is left with them to spend on other items?

In a village, there are 8 water tanks to collect rain water. On a particular day, x litres of rain water is collected per tank. If 100 litres of water was already there in one of the tanks, what is the total amount of water in the tanks on that day?

What is the area of a square whose side is m cm?

Perimeter of a triangle is found by using the formula P = a + b + c, where a, b and c are the sides of the triangle. Write the rule that is expressed by this formula in words.

Perimeter of a rectangle is found by using the formula P = 2 ( l + w), where l and w are respectively the length and breadth of the rectangle. Write the rule that is expressed by this formula in words.

On my last birthday, I weighed 40kg. If I put on m kg of weight after a year, what is my present weight?

Length and breadth of a bulletin board are r cm and t cm, respectively.

(i) What will be the length (in cm) of the aluminium strip required to frame the board, if 10cm extra strip is required to fix it properly.

(ii) If x nails are used to repair one board, how many nails will be required to repair 15 such boards?

(iii) If 500sqcm extra cloth per board is required to cover the edges, what will be the total area of the cloth required to cover 8 such boards?

(iv) What will be the expenditure for making 23 boards, if the carpenter charges Rs x per board.

Sunita is half the age of her mother Geeta. Find their ages

(i) after 4 years?

(ii) before 3 years?

Match the items of Column I with that of Column II: