# Linear Equations

### Ena was born 4 years after her parents' marriage

Ena was born 4 years after her parents' marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena's father get married?

1. 22 years
2. 23 years
3. 24 years
4. 25 years

### If x is greater than or equal to 25 and y is less than or equal to 40

If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct?

1. x is greater than y
2. (y - x) is greater than 15
3. (y - x) is less than or equal to 15
4. (x - y) is greater than or equal to 65

### The pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0

The pair of linear equations kx + 3y + 1 = 0 and 2x + y + 3 = 0 intersect each other, if

1. k = 6
2. k ≠ 6
3. k = 0
4. k ≠ 0

### Leela got married 6 years ago. Today her age is 1¼ times her age at the time of her marriage

Leela got married 6 years ago. Today her age is 1¼ times her age at the time of her marriage. Her son’s age is 1/10 times her age. What is the present age of her son?

1. 1 year
2. 2 years
3. 3 years
4. 4 years

### Sunil wants to spend Rs.200 on two types of sweets, costing Rs.7 and Rs.10 respectively

Sunil wants to spend Rs.200 on two types of sweets, costing Rs.7 and Rs.10 respectively. What is the maximum number of sweets he can get so that no money is left over?

1. 25
2. 26
3. 27
4. 28

### The system of equations 2x + 4y = 6 and 4x + 8y = 8 is

The system of equations 2x + 4y = 6 and 4x + 8y = 8 is

1. Consistent with a unique solution
2. Consistent with infinitely many solutions
3. Inconsistent
4. None of the above

### X paid Rs. 47 for certain cups of tea and coffee. If tea costs Rs. 5 per cup

X paid Rs. 47 for certain cups of tea and coffee. If tea costs Rs. 5 per cup and coffee costs Rs. 8 per cup, which one of the following statements is correct?

1. He drank 8 cups of tea and coffee.
2. He drank the same number of cups of tea and coffee.
3. He drank more tea than coffee.
4. He drank more coffee than tea.

### In a parking area, the total number of wheels of all the cars

In a parking area, the total number of wheels of all the cars (four-wheelers) and scooters/motorbikes (two-wheelers) is 100 more than twice the number of parked vehicles. The number of cars parked is

1. 35
2. 45
3. 50
4. 55

### In a box of marbles, there are three less white marbles

In a box of marbles, there are three less white marbles than the red ones and five more white marbles than the green ones. If there are a total of 10 white marbles, how many marbles are there in the box?

1. 28
2. 36
3. 26
4. 32

### Each of A, B, C and D has Rs 100. A pays Rs 20 to B

Each of A, B, C and D has Rs 100. A pays Rs 20 to B, who pays Rs 10 to C, who gets Rs 30 from D. In this context, which one of the following statements is not correct?

1. D is the poorest
2. C is the richest
3. B is richer than D
4. C has more than what A and D have together

### A person ordered 5 pairs of black socks and some pairs of brown socks

A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair. While preparing the bill, the bill clerk interchanged the number of black and brown pairs by mistake which increased the bill by 100%. What was the number of pairs of brown socks in the original order?

1. 15
2. 25
3. 10
4. 20

### A father is nine times as old as his son and the mother is eight times

A father is nine times as old as his son and the mother is eight times as old as the son. The sum of the father's and the mother's age is 51 years. What is the age of the son?

1. 3 years
2. 4 years
3. 7 years
4. 5 years

### A cow costs more than 4 goats but less than 5 goats

A cow costs more than 4 goats but less than 5 goats. If a goat costs between Rs. 600 and Rs. 800, which of the following is a most valid conclusion?

1. A cow costs between Rs. 2,600 and Rs. 3,800.
2. A cow costs less than Rs. 3,600.
3. A cow costs more than Rs. 2,500.
4. A cow costs between Rs. 2,400 and Rs. 4,000.

### A person has only Rs. 1 and Rs. 2 coins with her

A person has only Rs. 1 and Rs. 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs. 75, then the number of Rs. 1 and Rs. 2 coins are, respectively.

1. 30 and 20
2. 35 and 15
3. 25 and 25
4. 15 and 35

### Rakesh and Rajesh together bought 10 balls and 10 rackets

Rakesh and Rajesh together bought 10 balls and 10 rackets. Rakesh spent Rs. 1300 and Rajesh spent Rs. 1500. If each racket costs three times a ball does, then what is the price of a racket?

1. Rs. 70
2. Rs. 90
3. Rs. 210
4. Rs. 240

### In 2002, Meenu's age was one-third of the age of Meera

In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera. What is Meenu's year of birth?

1. 1992
2. 1994
3. 1996
4. 1998

### Consider the system of linear equation: x1 + 2x2 + x3 = 3

Consider the system of linear equation

x1 + 2x2 + x3 = 3

2x1 + 3x2 + x3 = 3

3x1 + 5x2 + 2x3 = 1

The system has

1. Infinite no. of solutions
2. No solution
3. Unique solution
4. Exactly 3 solutions

### The number of solutions of the equation 2x + y = 40 where both x and y

The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is:

1. 7
2. 13
3. 14
4. 18

### Three times the first of three consecutive odd integers is 3 more than twice

Three times the first of three consecutive odd integers is 3 more than twice the third. What is the third integer?

1. 5
2. 9
3. 11
4. 15

### Which one of the following conditions must p, q and r satisfy so that the following system

Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that p + q + r ≠ 0?

• x + 2y - 3z = p
• 2x + 6y - 11z = q
• x - 2y + 7z = r
1. 5p - 2q - r = 0
2. 5p + 2q + r = 0
3. 5p + 2q - r = 0
4. 5p - 2q + r = 0

### If x and y are integers, then the equation 5x + 19y = 64 has

If x and y are integers, then the equation 5x + 19y = 64 has

1. A solution for -59 < y < -56
2. No solution for x > 250 and y > -100
3. A solution for 250 < x < 300
4. No solution for x < 300 and y < 0

### Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins

Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs. 1.01 to three different persons?

1. 17
2. 18
3. 19
4. 20

### What is the value of k for which the following system of equations has no solution: 2x - 8y = 3 and kx + 4y = 10

What is the value of k for which the following system of equations has no solution: 2x - 8y = 3 and kx + 4y = 10.

1. 2
2. -2
3. -1
4. 1

### Two oranges, three bananas and four apples cost Rs.15. Three oranges, two bananas

Two oranges, three bananas and four apples cost Rs.15. Three oranges, two bananas and one apple cost Rs.10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay?

1. Rs 8
2. Rs 10
3. Rs 12
4. Rs 15

### In 2004, Rohini was thrice as old as her brother Arvind

In 2004, Rohini was thrice as old as her brother Arvind. In 2014, Rohini was only six years older than her brother. In which year was Rohini born?

1. 1984
2. 1986
3. 1995
4. 2000

### A firm is thinking of buying a printer for its office use for the next one year

A firm is thinking of buying a printer for its office use for the next one year. The criterion for choosing is based on the least per-page printing cost. It can choose between an inkjet printer which costs Rs. 5000 and a laser printer which costs Rs. 8000. The per-page printing cost for an inkjet is Rs. 1.80 and that for a laser printer is Rs. 1.50. The firm should purchase the laser printer, if the minimum number of a pages to be printed in the year exceeds

1. 5000
2. 10000
3. 15000
4. 18000

### Hari’s family consisted of his younger brother (Chari), younger sister (Gouri)

Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.

1. 5 years
2. 6 years
3. 7 years
4. 8 years
5. 9 years

### The captain of a cricket team of 11 members is 26 years old and the wicket keeper

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

1. 22 years
2. 23 years
3. 24 years
4. 25 years

### The number of positive integer valued pairs (x, y) satisfying 4x - 17y = 1 and x ≤ 1000 is

The number of positive integer valued pairs (x, y) satisfying 4x - 17y = 1 and x ≤ 1000 is

1. 55
2. 57
3. 58
4. 59

### Consider a triangle drawn on the X-Y plane with its three vertices of (41, 0), (0, 41) and (0, 0)

Consider a triangle drawn on the X-Y plane with its three vertices of (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

1. 741
2. 780
3. 800
4. 820

### A shop, which sold same marked price shirts, announced an offer

A shop, which sold same marked price shirts, announced an offer - if one buys three shirts then the fourth shirt is sold at a discounted price of ₹100 only. Patel took the offer. He left the shop with 20 shirts after paying ₹20,000. What is the marked price of a shirt?

1. ₹1260
2. ₹1300
3. ₹1350
4. ₹1400
5. ₹1500