Class 10 Pearson - Linear Equations in Two Variables (Mathematics)Contact Number: 8527521718Class 10 Pearson - Linear Equations in Two Variables (Mathematics)Contact Number: 8527521718For what value of k do the equations 3(k-1)x+4y=24 and 15x+20y=8(k+13) have infinite solutions?
1. 1
2. 4
3. 3
4. 2
If the system of equations 4x+py=21 and px-2y=15 has unique solution, then which of the following could be the value of p?
(A) 103 (B) 105
(C) 192 (D) 197
1. Both (A) and (B)
2. Both (C) and (D)
3. (A), (B) and (D)
4. All of (A), (B), (C) and (D)
If the system of equations is inconsistent, which of the following cannot be the value of p?
1. -24
2. -18
3. -12
4. -36
The semi-perimeter of a triangle exceeds each of its side by 5, 3 and 2 respectively. What is the perimeter of the triangle?
1. 12
2. 10
3. 15
4. 20
If (p, p) is the solution of system of equations ax+ by + (t-s)=0 and bx+ay+(s-r)=0, (ab), then which of the following must be true?
1. 2r = s+t
2. 2t = r+s
3. 2s = r+t
4. r+s+t = 0
If 173x+197y=149 and 197x+173y=221, then find (x, y).
1. (3, -2)
2. (2, 1)
3. (1, -2)
4. (2, -1)
Mallesh has some cows and some hens in his shed. The total number of legs is 92 and the total number of heads is 29. Find the number of cows in his shed.
1. 12
2. 14
3. 17
4. 19
The total cost of 14 pens and 21 books is ₹130 and the total cost of 6 pens and p books is ₹90. Which of the following cannot be the value of p?
1. 8
2. 9
3. 10
4. 11
If an ordered pair satisfying the equation 2x-3y=18 and 4x-y=16 also satisfies the equation 5x-py-23=0, then find the value of p.
1. 1
2. 2
3. -1
4. -2
If are such that are consecutive integers in the same order, then find the values of x and y.
1. 1, -2
2. 2, -3
3. 1, 3
4. -1, 1
If we increase the length by 2 units and the breadth by 2 units, then the area of rectangle is increased by 54 square units. Find the perimeter of the rectangle (in units).
1. 44
2. 50
3. 56
4. 52
A mother said to her son, 'the sum of our present ages is twice my age 12 years ago and nine years hence, the sum of our ages will be thrice my age 14 years ago'. What is her son's present age? (in years)
1. 8
2. 12
3. 15
4. 10
A told B, 'when I was as old as you are now, then your age was four years less than half of my present age'. If the sum of the present ages of A and B is 61 years, what is B's present age? (in years)
1. 9
2. 25
3. 43
4. 36
If the system of equations 4x-5y=6 and -12x+ay=b is inconsistent, which of the following cannot be the value of b?
1. -16
2. -18
3. -20
4. -22
Dheeraj has twice as many sisters as he has brothers. If Deepa, Dheeraj's sister has the same number of brothers as she has sisters, then Deepa has how many brothers?
1. 2
2. 3
3. 4
4. 6
The total cost of six books, five pencils and seven sharpeners is ₹115 and that of eight books, ten pencils and fourteen sharpeners is ₹190, then which of the following article's cost can be found uniquely?
1. Book
2. Pencil
3. Sharpener
4. None of these
The sum of the speeds of a boat in still water and the speed the current is 10 kmph. If the boat takes 40% of the time to travel downstream when compared to that upstream, then find the difference of the boat when travelling upstream and down stream.
1. 3 kmph
2. 6 kmph
3. 4 kmph
4. 5 kmph
In a fraction, if the numerator is decreased by 1 and the denominator is increased by 1, then the fraction becomes Instead, if the numerator is increased by 1 and the denominator is decreased by 1, then the fraction becomes Find the numerator of the fraction.
1. 5
2. 6
3. 7
4. 8
Ram has 18 coins in the denominations of ₹1, ₹2 and ₹5. If their total value is ₹54 and the number of ₹2 coins are greater than that of ₹5 coins, then find the number of ₹1 coins with him.
1. 2
2. 3
3. 4
4. 1
If the ordered pair satisfies the system of equations mx+my+a+b=a-b and nx+my+2b=0, then find the value of where
1. 30
2. 45
3. 50
4. 60
Swaroop can row 16 km downstream and 8km upstream in 6 hours. He can row 6 km upstream and 24 km downstream in 6 hours. Find the speed of Swaroop in still water.
1. 6 kmph
2. 8 kmph
3. 3 kmph
4. 5 kmph
A two-digit number is formed by either subtracting 17 from nine times the sum of the digits or bu adding 21 to 13 times the difference of the digits. Find the number.
1. 37
2. 73
3. 71
4. 72
Swathi starts her job with certain monthly salary and earns a fixed increment every year. If her salary was ₹22500 per month after 6 years of service and ₹30000 per month after 11 years of service. Find her salary after 8 years of service (in ₹).
1. 24000
2. 25500
3. 26000
4. 24500
A three digit number abc is 459 more than the sum of its digits. What is the sum of the 2-digit number ab and the 1-digit number a?
1. 71
2. 61
3. 51
4. 41
The following sentences are the steps involved in solving the inequation |5x+4|>5x-4. Arrange in sequential order from first to last.
(A) 10x<0 (B) 5x+4<-5x+4 or 5x+4>5x-4
(C) x<0 (D) 5x+4<-5x+4
1. BDAC
2. DBAC
3. ABDC
4. BADC
The following sentences are the steps involved in solving the inequation 5x+2>7x-4. Arrange them in sequential order from first to last.
(A) Solution set = {0, 1, 2} (B)
(C) (D)
1. CBAD
2. BCDA
3. CBDA
4. BCAD
The total cost of 6 erasers and 9 pens is at least ₹102 and the cost of each eraser is at most ₹5. Find the minimum possible cost (in rupees) of a pen. The following are the steps involved in solving the above problem. Arrange them in sequential order.
(A) Let the cost of each eraser be ₹x and cost of each pen be ₹y.
(B)
(C)
(D) The minimum possible cost of a pen is ₹8.
1. ABDC
2. ABCD
3. DABC
4. ACBD
An examination consists of 100 questions. Two marks are awarded for every correct option. If one mark is deducted for every wrong option and half mark is deducted for every question left, then a person scores 135. Instead, if half mark is deducted for every wrong option and one mark is deducted for every question left, then the person scores 133. Find the number of questions left unattempted by the person.
1. 14
2. 16
3. 10
4. 12
Ram, Shyam, Tarun and Varun together had a total amount of ₹240 with them. Ram had half of the total amount with the others. Shyam had one-third of the total amount with the others. Tarun had one-fourth of the total amount with the others. Find the amount with Varun (in ₹).
1. 64
2. 70
3. 52
4. 58
Ramu had 13 notes in the denominations of ₹10, ₹50 and ₹100. The total value of the notes with him was ₹830. He had more of ₹100 notes than that of ₹50 notes with him. Find the number of ₹10 notes with him.
1. 4
2. 3
3. 2
4. 5
A, B, C and D share a certain amount amongst themselves. B sees that the other three get 3 times what he himself gets. C sees that the other three get 4 times what he gets, while D sees that the other three get 5 times what he gets. If the sum of the largest and smallest shares is 99, what is the sum of the other two shares?
1. 99
2. 81
3. 64
4. 54
If 3|x|+5|y|=8 and 7|x|-3|y|=48, then find the value of x+y.
1. 5
2. -4
3. 4
4. The value does not exist
The cost of 2 puffs, 14 cups of coffee and 5 pizzas is ₹356. The cost of 20 puffs, 7 cups of coffee and 15 pizzas is ₹830. Find the cost of 38 puffs and 25 pizzas. (in ₹)
1. 1296
2. 1104
3. 1304
4. 1034
A father's present age is 6 times his son's present age. Thirty years hence the father's age will be ten years less than twice the son's age. After how many years will the son's age be half of the father's present age?
1. 20
2. 30
3. 10
4. 15
Ramesh had a total of 30 coins in his purse of denominations ₹5 and ₹2. If the total amount with him is ₹120, then find the number of ₹5 coins.
1. 20
2. 10
3. 4
4. 12
Mukesh has some goats and hens in his shed. Upon counting, Mukesh found that the total number of legs is 112 and the total number of heads is 40. Find the number of hens in his shed.
1. 18
2. 20
3. 22
4. 24
If the length and breadth of a room are increased by 1m each, its area would increase by 31 m2. If the length is increased by 1m and breadth is decreased by 1m, the area would decrease by 9 m2. Find the area of the floor of the room, in m2.
1. 200
2. 209
3. 250
4. 199
A hybrid mango tree, whose life span is 10 years, starts giving fruits from the first year onwards. In the nth year it produces 11n raw mangoes. But during the first half of the tree's life, every year, a certain number, which is constant, fail to ripen into fruits. During the second half of the tree's life, every year, the number of raw fruits that fail to ripen is half the corresponding number in the first half of the tree's life. In the fourth year of the tree's life, it produces 36 ripe mangoes. How many mangoes ripen during the 9th year of the tree's life?
1. 100
2. 96
3. 95
4. 86
A teacher wanted to distribute 900 chocolates among the students of a class. Each boy received 12 chocolates and each girl received 6 chocolates. If each girl had been given 10 chocolates, then each number of boy would have received 5 chocolates. Find the number of students in the class.
1. 80
2. 90
3. 100
4. 110
Sridevi purchased cakes of two varieties of soap. Lux and Dove, spending a total ₹360. If each Lux costs ₹30 and each Dove cost ₹40, then in how many different combinations could she have purchased the cakes?
1. 3
2. 4
3. 5
4. 2
Venu has as many sisters as he has brothers. If Karuna, Venu's sister has thrice as many brothers as she has sisters, then Venu has how many sisters?
1. 1
2. 2
3. 3
4. 4
The cost of two pencils, five erasers and eight sharpeners is ₹47. The cost of three pencils, three erasers and seven sharpeners is ₹42. Find the cost of twelve pencils, three erasers and eighteen sharpeners. (in ₹)
1. 37
2. 92
3. 138
4. 111
Total cost of 15 erasers and 25 pencils is ₹185 and the total cost of 9 erasers and x pencils is ₹106. Which of the following cannot be the value of x?
1. 12
2. 10
3. 13
4. 15
In a fraction, if the numerator is decreased by 1 and the denominator is increased by 1, then the resulting fraction is . Instead, if the numerator is increased by 1 and the denominator is decreased by 1, then the resulting fraction is . Find the difference between the numerator and the denominator of the fraction.
1. 2
2. 3
3. 4
4. 5
A two-digit number is such that, it exceeds the sum of the number formed by reversing the digits and sum of the digits by 4. Also, the original number exceeds the reversed number by 18. Find the product of the digits.
1. 48
2. 36
3. 42
4. 56
Bhanu has a total of 40 coins of denominations 30 paise and 10 paise. The total amount with him is ₹9. Find the number of 10 paise coins with him.
1. 25
2. 35
3. 15
4. 20
A father's present age is seven years less than 30 times of what his son's age was 20 years ago. Also, the father's present age is 31 yeats more than his son's present age. Find the sum of their present ages, in years.
1. 75
2. 74
3. 73
4. 72
A and B, have some coins. If A gives 100 coins to B, then B will have twice the number of coins left with A. Instead, if B gives 40 coins to A, then A will have thrice the number of coins left with B. How many more coins does A have than B?
1. 64
2. 88
3. 75
4. 96
Snehal can row 28 km downstream and 12 km upstream in 5 hours. He can row 21 km downstream and 10 km upstream in 4 hours. Find the speed of Snehal in still water.
1. 9 kmph
2. 8 kmph
3. 6 kmph
4. 5 kmph
The ratio of monthly incomes of Mr X and Mr Y is 3 : 4 and the ratio of their monthly expenditures is 5 : 7. If the ratio of their monthly savings is 3 : 2 and Mr X saves ₹500 more than Mr Y per month, then find the monthly income of Mr Y is
1. ₹35000
2. ₹32000
3. ₹26000
4. ₹22000
A two-digit number is seven times the sum of its digits. The number formed by reversing the digits is 6 more than half of the original number. Find the difference of the digits of the given number.
1. 2
2. 3
3. 4
4. 5
Sanjana travels 660 km, partly by train and partly by car. If she covers 300 km by train and the rest by car, it takes 13.5 hours. But, if she travels 360 km by train the rest by car, she takes 30 minutes longer. Find the time taken by Sanjana if she travels 660 km by car. (in hours)
1. 13
2. 14
3. 12
4. 11
In a test of 50 questions, each correct answer fetches two marks and each wrong answer fetches marks. A candidate attempted all the questions and scored 40 marks. How many questions did he attempt correctly?
1. 24
2. 26
3. 22
4. 20
The average weight of the students in a class is 60 kg. If eight new students of average weight 64 kg join the class, the average weight of the entire class becomes 62 kg. How many students were there in the class initially?
1. 12
2. 10
3. 8
4. 14