Equations

Q.

The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. what is the age of the youngest child?

1. 4 years

2. 8 years

3. 10 years

4. 11 years

5. 16 years

Q.

A test has 50 questions. A student scores 1 mark for a correct answer, $\frac{-1}{3}$ for a wrong answer, and $\frac{-1}{6}$ for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than

1. 6

2. 5

3. 3

4. 2

Q. A two -digit number is such that the product of the digits is 14. When 45 is added to the number, then the digits interchange their places. Find the number.

1. 72
2. 37
3. 27
4. 14

Q.

A sum of Rs.312 was divided among 100 boys and girls in such a way that each boy gets Rs.3.60 and each girl, Rs.2.40. The number of girls is?

1. 40

2. 100

3. 60

4. 20

5. 80

Q. I am three times as old as my son. 5 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?

1. None of these
2. 45 years, 15 years
3. 40 years, 10 years
4. 60 years, 25 years
5. 50 years, 20 years

Q. In a class, there are 20 boys whose average age is decreased by 2 months, when one boy aged 18 years in replaced by a new boy. The age of the new boy is:

1. 14 years and 8 months
2. 15 years
3. 16 years 4 months
4. 17 years 10 months
5. None of these

Q.

The ratio of incomes of A and B is 5:4 and the ratio of expenditure is 3:2. If at the end of the year each saves Rs 1600, then the income of B is?

1. 1600

2. 3200

3. 2400

4. 4800

5. none

Q.

The average age of 14 girls and their teacher's age is 15 years. If the teacher's age is excluded, then the average is reduced by 1. What is the teacher's age?

1. 29 years
2. 35 years
3. 32 years
4. 30 years
5. None of these

Q. A two digit number is such that the product of its digits is 12. When 9 is added to the number, the digits interchange their places. The number is ___.

Q.

The average age of 36 students in a class is 14 years. When their teacher's age is included to it, the average increases by one. What is the teacher's age in years?

1. 45

2. 51

3. 54

4. 56

5. 48

Q. The sum of 4 consecutive two-digit odd numbers, when divided by 10 becomes a perfect square. Which of the following can possibly be one of these 4 numbers?

1. 23

2. 75

3. 87

4. 49

Q. In an examination, there are 30 questions, 1 mark is given for each correct answer and 0.25 is deducted for every incorrect answer. Ankur attempted all the questions and scored 13.75 How many incorrect answers did he have?

1. 10
2. 11
3. 12
4. None of these

Q.

X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

1. 6 days

2. 15 days

3. 20 days

4. 16 days

5. 10 days

Q.

If the length and breadth of a rectangular room are each increased by 1 m, then the area of floor is increased by 21 sq.m. If the length is increased by 1 m and breadth is decreased by 1 m, then the area is decreased by 5 sq.m. The perimeter of the floor is:

1. 30 m

2. 32 m

3. 40 m

4. 36 m

5. 45 m

Q.

For $\frac{\left(\right|x-1\left|\right)}{(x+2)}-1<0$, $x$ lies in the interval

1. $(-\infty ,–2)\cup (-\frac{1}{2},\infty )$

2. $(-\infty ,1)\cup (2,3)$

3. $(-\infty ,–4)$

4. $(-\frac{1}{2},1)$

Q.

If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 5/8 and if the numerator and denominator of the same fraction are each increased by 1, the fraction becomes 1/2. Find the fraction.

1. 2/5

2. None of these

3. 2/7

4. 3/7

5. 4/5

Q. Find the value of k for which the system:
kx + 2y = 5, 3x + y = 1 has a unique solution

1. $k=6$
2. $k\ne 9$
3. $k\ne 6$
4. $k=6$
5. None of these

Q. A young girl Roopa leaves home with x flowers goes to the bank of a nearby river. On the bank of the river, there are four places of worship, standing in a row. She dips all the x flowers into the river, the number of flowers doubles. Then she enters the first place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the second place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the third place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the fourth place of worship, offers y flowers to the deity. Now she is left with no flowers in hand.

The minimum number of flowers that could be offered to each deity is:

1. 0
2. 15
3. 16
4. cannot be determined

Q.

How many two-digit numbers satisfy the property, 'The last digit (unit’s digit) of the square of the two-digit number is 8'?

1. 2

2. 1

3. 3

4. 0

5. 4

Q.

The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:

1. 2480 m²

2. 2520 m²

3. 2590 m²

4. 1520 m²

5. 2420 m²

Q. 3 years ago, the average age of A, B, and C was 27 years. Also 5 years ago, the average age of B and C was 20 years.
What is the present age of A?

1. 40
2. 34
3. 35
4. None of these
5. 42

Q. A student was asked to divide a number by 6 and add 12 to the quotient. He, however, first added 12 to the number and then divided it by 6, got 112 as the answer. The correct answer should have been:

1. 114
2. None of the above
3. 124
4. 122
5. 118

Q. The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and $x\le y$

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

Q. For a positive integer n, let $P_n$ denote the product of the digits of n and $S_n$ denote the sum of the digits of n. The number of integers between 10 and 1000 for which $P_n+S_n=n$ is:

1. 9
2. 16
3. 18
4. 81

Q.

The hotel bill for a certain number of people for an overnight stay is Rs.4800. If there were 4 more, the bill each person had to pay would have been reduced by Rs.200. Find the number of people staying overnight.

1. None of these

2. 10

3. 12

4. 8

Q. A boy bought 3 apples, 5 mangos and 8 bananas for Rs.87. Had he bought 5 apples 7 Mangos and 6 Bananas, it would cost him Rs.121. By how much would an apple and a mango together cost more than a banana?

1. Rs. 15
2. Rs. 17
3. Rs. 19
4. Rs. 20

Q. A number consists of three digits whose sum is 10. The middle digit is equal to sum of the other two and when the number is increased by 99, the first digit and the third digit get interchanged. The digit in the hundreds place is

1. 5
2. 4
3. 2
4. 3

Q. The ratio of incomes of A and B is 9 : 7 and the ratio of their expenditures is 4 : 3. Find the sum of their monthly incomes if each of them manages to save Rs.4000 per month.

1. Rs.64000
2. Rs.36000
3. Rs.28000
4. Rs.68000
5. Rs.60000

Q. The digit in the unit's place of a number is equal to the digit in the tens' place of half of that number and the digit in the tens' place of that number is less than the digit in unit's place of half of the number by 1. If the sum of the digits of the number is seven, then what is the number?

1. Data inadequate
2. 52
3. 16
4. 34

Q.

A number consists of two digits. If the digits interchange places and the new number is added to the original number; then the resulting number will be divisible by:

1. 3

2. 5

3. 9

4. 11

5. 16