INDRAGYAN CLASSES

Class – X
1. Akhila went to a fair in her village. She wanted to enjoy rides on the Giant wheel and play
Hoopla (a game in which you throw a rig on the items kept in the stall , and if the ring covers
any object completely you get it). The number of times she played Hoopla is half the number
of rides she had on the Giant wheel. Each ride costs ₹ 3, and a game of Hoopla costs ₹ 4. If
she spent ₹ in the fair, represent this situation algebraically and graphically.
Ans. 𝑥 − 2𝑦 = 0, 3𝑥 + 4𝑦 = 20
2. Solve the following system of linear equations graphically.
x - y = 1 and 2x + y = 8
Shade the area bounded by these two lines and y – axis. Also, determine this area.
Ans. 13.5 sq. units.
3. Determine graphically the vertices of a trapezium, the equations of whose sides are: 𝑥 =
0, 𝑦 = 0, 𝑦 = 4 and 2𝑥 + 𝑦 = 6 Also, determine its area. Ans. 8sq. units
4. Champa went to ‘sale’ to purchase some pants and skirts. When her friend asked her how
many of each she had bought, she answered, “The number of skirts is two less then twice the
number of pants purchased. Also, the number of skirts is four less then four times the number
of pants purchased”. Help her friend to find how many pants and skirt Champa bought.
Ans. Pant =1, skirt = 0
𝑥 7
5. Solve + 𝑦 = 0.8 𝑦 = 10 Ans. 𝑥 = 0.4, 𝑦 = 0.6𝑠
2 𝑥+
2
6. If 𝑥 + 1is a factor of 2𝑥 3 + 𝑎𝑥 2 + 2𝑏𝑥 + 1, then find the values of a and b given that
2𝑎 − 3𝑏 = 4. Ans. 𝑎 = 5, 𝑏 = 2
7. Find the values of 𝑥 and 𝑦 in the following rectangle.
x+3y
D C
3x+y 7

A B
13 Ans. 𝑥 = 1, 𝑦 = 4
8. Write an equation of a line passing through the point representing solution of the pair of
linear equations 𝑥 + 𝑦 = 2 and 2𝑥 − 𝑦 = 1. How many such lines can we find?
Ans. 3𝑥 + 2𝑦 = 5, Infintely many
9. Write a pair of linear equations which has the unique solution 𝑥 = −1, 𝑦 = 3. How many
such pairs can you write? Ans. 12𝑥 + 5𝑦 = 3, Infintely many
10. Find the value of K for which the following system of equations has a unique solution:
𝑘𝑥 + 2𝑦 = 5 , 3𝑥 + 𝑦 = 1 Ans. 𝑘 ≠ 6
11. 4𝑥 − 5𝑦 = 𝑘 2𝑥 − 3𝑦 = 12 Ans. 𝑘 is any real number
12. 2𝑥 + 3𝑦 = 2 (𝑘 + 2)𝑥 + (2𝑘 + 1)𝑦 = 2(𝑘 − 1) Ans. 𝑘 = 4
13. 𝑥 + (𝑘 + 1)𝑦 = 4 (𝑘 + 1)𝑥 + 9𝑦 = 5𝑘 + 2 Ans. 𝑘 = 2
14. 𝑘𝑥 − 5𝑦 = 2 6𝑥 + 2𝑦 = 7 Ans. 𝑘 = −15
15. 𝑘𝑥 + 3𝑦 = 𝑘 − 3 12𝑥 + 𝑘𝑦 = 6 Ans. 𝑘 = −6
16. Obtain the condition for the following system of linear equations to have a unique solution
𝑎𝑥 + 𝑏𝑦 = 𝑐 , 𝑙𝑥 + 𝑚𝑦 = 𝑛 Ans. 𝑎𝑚 ≠ 𝑏𝑙
17. A and B each have certain number of oranges. A says to B, “if you give me 10 of your
oranges, I will have twice the number of oranges left with you. “B replies, “if you give me 10
of your oranges, I will have the same number of oranges as left with you”. Find the number
of oranges with A and B separately. Ans. A has 70 oranges and B has 50 oranges.
18. Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and
5 less pens, then number of pencil would become 4 times the number of pens. Find the
original number of pens and pencils. Ans. No. of pens = 13, No of pencils = 27
19. Jamila sold a table and a chair for ₹1050, thereby making a profit of 10% on a table and
25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair she
would have got ₹1065. Find the cost price of each. Ans. Table ₹500, chair ₹400
20. Susan invested certain amount of money in two schemes A and B, which offer interest at
the rate of 8% per annum and 9% per annum, respectively. She received ₹1860 as annual
interest. However, had she interchanged the amount of investment in the two schemes, she
would have received ₹20 more as annual interest. How much money did she invest in each
scheme? Ans. 10000 in scheme A, ₹12000 in scheme B
21. The cost of 4 pens and 4 pencil boxes is ₹100. Three times the cost of a pen ₹15 more then
the cost of a pencil box. Form the pair of linear equations for the above situation. Find the
cost of a pen and a pencil box. Ans. ₹10, ₹15
22. Vijay had some bananas, and he divided them into two lots A and B. He sold first lot at
the rate of ₹ 2 for 3 bananas and the second lot at the rate of ₹1per banana and got a total of
₹400. If he had sold the first lot at the rate of ₹1per banana and the second lot at the rate of
₹4per five bananas, his total collection would have been ₹460. Find the total number of
bananas he had. Ans. 500
23. On selling a T.V at 5% gain and a fridge at 10% gain, a shopkeeper gains ₹2000. But if he
sells the T.V. at 10% gain and the fridge at 5% loss. He gains ₹1500 on the transaction. Find
the actual prices of T.V. and fridge. Ans. ₹20,000, ₹10, 000
24. In a two digit number, the ten’s digit is three times the unit’s digit. When the number is
decreased by 54, the digits are reversed. Find the number. Ans.93
25. The sum of a two digit number and the number obtained by reversing the order of its digits
is 121, and the two digits differ by 3. Find the number. Ans. 47 or, 74.
26. The sum of a two digit number and the number formed by interchanging its digits is 110.
If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of
the digits in the first number. Find the first number. Ans. 64
27. A two digit number is obtained by either multiplying sum of the digits by 8 and adding 1
or by multiplying the difference of the digits by 13 and adding 2. Find the number. Ans. 41
28. If three times the larger of the two number is divided by the smaller one, we get 4 as
quotient and 3 as the remainder. Also, if seven times the smaller number is divided by the
larger one, we get 5 as quotient and 1 as remainder. Find the numbers. Ans. 25and 18.
29. A two – digit number is 4 times the sum of its digits and twice the product of the digits.
Find the number. Ans. 36

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30. A two – digit number is such that the product of its digits is 20. If 9 is added to the
number. The digits interchange their places. Find the number. Ans. 45
31. Two number are in the ratio 5:6. If 8 is subtracted form each of the numbers, the ratio
becomes 4:5. Find the number. Ans. 40, 48
32. The denominator of a fraction is 4 more than twice the numerator. When both the
numerator and denominator are decreased by 6, then the denominator becomes 12 times the
7
numerator. Determine the fraction. Ans.
18
33. The sum of the numerator and denominator of a fraction is 4 more than twice the
numerator. If the number and denominator are increased by 3, they are in the ratio 2:3.
5
Determine the fraction. Ans.
9
34. The sum of the numerator and denominator of a fraction is 3 less than twice the
denominator. If the numerator and denominator are decreased by 1, the numerator becomes
4
half the denominator. Determine the fraction. Ans.
7
35. If twice the son’s age in years is added to the father’s age, the sum is 70. But if twice the
father’s age is added to the son’s age, the sum is 95. Find the ages of father and son.
Ans. 40 years, 15 years.
36. I am three time as old as my son. Five years later, I shall be two and a half times as old as
my son. How old am I and how old is my son. Ans. 45 years, 15 years.
37. Father’s age is three times the sum of ages of his two children. After 5 years his age well
be twice the sum of ages of two children. Find the age of father. Ans. 45 years
38. X takes 3 hours more than Y to walk 30 Km. But, if X doubles his pace, he is ahead of Y
1 10
by 1 hours. Find their speed of walking. Ans. 𝐾𝑚/ℎ𝑟, 5Km / hr.
2 3
39. After covering a distance of 30 Km with a uniform speed there is some defect in a train
engine and therefore, its speed is reduced to 4/5 of its original speed. Consequently, the train
reach its destination late by 45 minutes. Had it happened after covering 18 Kilometres more,
the train would have reached 9 minutes earlier. Find the speed of the train and the distance of
journey. Ans. 30 Km / hr, 120 Km.
40. A man walks a certain distance with certain speed. If he walks 1/2 Km an hour faster, he
takes 1 hour less. But, if he walks 1Km an hour slower, he takes 3 more hours. Find the
distance covered by the man and his original rate of walking. Ans. 36Km, 4Km / hr.
41. A Person rowing at the rate of 5 Km / h in still water, takes thrice as much time in going
40 Km upstream as in going 40 Km downstream. Find the speed of the stream.
Ans. 2.5 Km/ hr
42. The total expenditure per month of a household consists of a fixed rent of the house and
mess charges depending upon the number of people sharing the house. The total monthly
expenditure is ₹3900 for 2 people and ₹7500 for 5 people. Find the rent of the house and the
mess charges per head per month. Ans. ₹1500, ₹1200
43. A man starts his job with a certain monthly salary and earns a fixed increment every year.
If his salary was ₹1500 after 4 year of service and ₹1800 after 10 years of service, what was
his starting salary and what is the annual increment? Ans. ₹1300 is ₹50.

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44. A man sold a chair and a table together for ₹1520 thereby making a profit of 25% on the
chair and 10% on table. By selling them together for ₹1535 he would have made a profit of
10% on the chair and 25% on the table. Find the cost price of each. Ans. ₹600, ₹700
45. Students of a class are made to stand in rows. If one student is extra in a row, there would
be 2 rows less. If one student is less in a row there would be 3 rows more. Find the number
of students in the class. Ans. 60.
46. On selling a tea – set at 5% loss and a lemon – set at 15% gain, a crockery seller gains ₹7.
If he sells the tea – set at 5% gain and the lemon – set 10% gain, he gains ₹13. Find the
actual price of the tea – set and the lemon – set. Ans. ₹100, ₹80
47. It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter
is used for four hours and the pipe of smaller diameter for 9 hours, only half of the pool can
be filled. How long would it take for each pipe to fill the pool separately?
Ans. 20 hours, 30 hours
48. There are two examination rooms A and B. If 10 candidates are sent from A to B, the
number of students in each room is same. If 20 candidates are sent from B to A, the number
of students in A is double the number of students in B. Find the number of students in each
room. Ans. 100, 48
49. A railway half ticket costs half the full fare and the reservation charge is the same on half
ticket as on full ticket. One reserved first class ticket from Mumbai to Ahmedabad costs
₹216 and one full and one half reserved first class tickets cost ₹327. What is the basic first
class full fare and what is the reservation charge?
Ans. Fare = ₹210, Reservation charge = ₹6
50. A Wizard having powers of mystic in candations and magical medicines seeing a cock,
fight going on, spoke privately to both the owners of cocks. To one he said; if your bird wins,
than you give me your stake – money, but if you do not win, I shall give you two third of
that. Going to the other, he promised in the same way to give three fourths. Form both of
them his gain would be only 12 gold coins. Find the stake of money each of the cock –
owners have. Ans. 42,40 Gold Conis.
51. A Shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby getting a
sum of ₹1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she
would have got ₹1028. Find the cost price of the saree and the list price (price before
discount) of the sweater. Ans. ₹600, ₹400
52. In a competitive examination, one mark is awarded for each correct answer while 1/2
mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks.
How many questions did she answer correctly. Ans. 100

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