LINEAR EQUATION PROBLEMS FOR VYOM
1. If you subtract 1 2 from a number
and multiply the result by 1 2 , you get 1 8 . What is the number?
2. The perimeter of a rectangular
swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are
the length and the breadth of the pool?
3. The base of an isosceles triangle
is 4 cm 3 . The perimeter of the triangle is 2 4 cm 15 . What is the length of
either of the remaining equal sides?
4. Sum of two numbers is 95. If one exceeds
the other by 15, find the numbers.
5. Two numbers are in the ratio 5:3.
If they differ by 18, what are the numbers?
6. Three consecutive integers add up
to 51. What are these integers?
7. The sum of three consecutive multiples of 8
is 888. Find the multiples.
8. Three consecutive integers are
such that when they are taken in increasing order and multiplied by 2, 3 and 4
respectively, they add up to 74. Find these numbers.
9. The ages of Rahul and Haroon are
in the ratio 5:7. Four years later the sum of their ages will be 56 years. What
are their present ages?
10. The number of boys and girls in
a class are in the ratio 7:5. The number of boys is 8 more than the number of
girls. What is the total class strength?
11. Baichung’s father is 26 years
younger than Baichung’s grandfather and 29 years older than Baichung. The sum
of the ages of all the three is 135 years. What is the age of each one of them?
12. Fifteen years from now Ravi’s
age will be four times his present age. What is Ravi’s present age?
13. A rational number is such that when you
multiply it by 5 2 and add 2 3 to the product, you get 7 12 − . What is the
number?
14. Lakshmi is a cashier in a bank. She has
currency notes of denominations Rs 100, Rs 50 and Rs 10, respectively. The
ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is Rs
4,00,000. How many notes of each denomination does she have?
15. I have a total of Rs 300 in
coins of denomination Re 1, Rs 2 and Rs 5. The number of Rs 2 coins is 3 times
the number of Rs 5 coins. The total number of coins is 160. How many coins of
each denomination are with me?
16. The organisers of an essay
competition decide that a winner in the competition gets a prize of Rs 100 and
a participant who does not win gets a prize of Rs 25. The total prize money
distributed is Rs 3,000. Find the number of winners, if the total number of participants
is 63.
Some more challenges...
1. Amina thinks of a number and
subtracts 5 2 from it. She multiplies the result by 8. The result now obtained
is 3 times the same number she thought of. What is the number?
2. A positive number is 5 times
another number. If 21 is added to both the numbers, then one of the new numbers
becomes twice the other new number. What are the numbers?
3. Sum of the digits of a two-digit
number is 9. When we interchange the digits, it is found that the resulting new
number is greater than the original number by 27. What is the two-digit number?
4. One of the two digits of a two
digit number is three times the other digit. If you interchange the digits of
this two-digit number and add the resulting number to the original number, you
get 88. What is the original number?
5. Shobo’s mother’s present age is
six times Shobo’s present age. Shobo’s age five years from now will be one
third of his mother’s present age. What are their present ages?
6. There is a narrow rectangular
plot, reserved for a school, in Mahuli village. The length and breadth of the
plot are in the ratio 11:4.At the rate Rs100 per metre it will cost the village
panchayat Rs 75000 to fence the plot. What are the dimensions of the plot?
7. Hasan buys two kinds of cloth
materials for school uniforms, shirt material that costs him Rs 50 per metre
and trouser material that costs him Rs 90 per metre. For every 2 meters of the
trouser material he buys 3 metres of the shirt material. He sells the materials
at 12% and 10% profit respectively. His total sale is Rs 36,660. How much
trouser material did he buy?
8. Half of a herd of deer are
grazing in the field and three fourths of the remaining are playing nearby. The
rest 9 are drinking water from the pond. Find the number of deer in the herd.
9. A grandfather is ten times older
than his granddaughter. He is also 54 years older than her. Find their present
ages.
10. Aman’s age is three times his
son’s age. Ten years ago he was five times his son’s age. Find their present
ages.