Mathematics - Simple Equations
Exam Duration: 45 Mins Total Questions : 30
What is the value of 'x' in \(\frac{3x-1}{5}-\frac{1+x}{2}=3-\frac{x-1}{2}?\)
- (a)
5
- (b)
-7
- (c)
7
- (d)
-5
If 0.2(2x - 1) - 0.5(3x -1) = 0.4, what is the value of 'x'?
- (a)
\(\frac{1}{11}\)
- (b)
\(-\frac{1}{11}\)
- (c)
\(\frac{3}{11}\)
- (d)
\(-\frac{3}{11}\)
Sunil wrote an equation as \(\frac{m}{5}=4\) Ravi wrote a statement for Sunil's equation.
Which of these is the statement of Ravi if he has written correctly?
- (a)
One-fifth of 'm' is 4.
- (b)
One-fifth of a number is 5.
- (c)
One-fourth of 'rn' is 4.
- (d)
One-fourth of a number is 4.
A number is3 less than two times the other. If their sum is increased by 7, the result is 37. Find the numbers.
- (a)
9,11
- (b)
11, 13
- (c)
11,19
- (d)
9,13
\(\frac{1}{2}\) is subtracted from a number and the difference is multiplied by 4.lf 25 is added to the product and the sum is divided by 3, the result is equal to 10. Find the number.
- (a)
\(\frac{3}{5}\)
- (b)
\(\frac{7}{4}\)
- (c)
\(\frac{6}{7}\)
- (d)
\(\frac{2}{3}\)
Which of the following is an algebraic expression for the statement "The sum of 3x and 11 is 32."?
- (a)
11x + 3 = 32
- (b)
3x + 11 = 32
- (c)
3x + 32 = 11
- (d)
11x + 32 = 11
Vinay's father is 44 years old. If he is 5 years older than thrice Vinay's age, which of these equations gives, the age of Vinay's father?
- (a)
3x + 5 = 44
- (b)
44 + 5x = 3x
- (c)
44-3y=5+3y
- (d)
3x-5=44
Which of the following statements is false?
- (a)
The solution of 4x = 60 is 12.
- (b)
y = 7 satisfies the equation y + 0 = 7.
- (c)
\(p=\frac{5}{2}\) is the solution of 12p - 5 = 25.
- (d)
\(m=\frac{3}{2}\)is the solution of 4(m + 3) = 18.
P is a linear equation. How many solutions does P have?
- (a)
1
- (b)
0
- (c)
3
- (d)
Infinitely many
Ramesh got 5 marks more than Sonu in a test. If the total marks secured by them is 15, how many marks did Ramesh get?
- (a)
25
- (b)
5
- (c)
15
- (d)
10
A teacher asks the students of her class to write an equation for the statement "Ten times a number p is 100." Three students wrote the following equations. Which is correct?
(i) 10 P = 100
(ii) \(\frac{10}{p}=100\)
(iii) \(\frac{10p}{p}=100\)
- (a)
(i) only
- (b)
(ii) only
- (c)
(iii) only
- (d)
Both (B) and (C).
\(M=\frac{2x+5}{7}\ and N=\frac{3x-2}{4}\) What value of x makes M = N?
- (a)
\(\frac{-17}{3}\)
- (b)
\(\frac{-34}{13}\)
- (c)
\(\frac{34}{13}\)
- (d)
\(\frac{17}{3}\)
Given A = P(1 + rt), what is the value of 'r' when A = 27, P = 18 and t = 5?
- (a)
\(\frac{1}{2}\)
- (b)
\(\frac{1}{5}\)
- (c)
\(\frac{27}{5}\)
- (d)
\(\frac{1}{10}\)
Given \(\frac{1}{u}+\frac{1}{v}=\frac{1}{f}\) find the value of 'v' when f = 20 and u = 30.
- (a)
-20
- (b)
-60
- (c)
60
- (d)
-30
A father is 26 years older than his son. In 3 years' time, the son's age will be one third his father's age. What is the present age of the son?
- (a)
10 years
- (b)
13 years
- (c)
39 years
- (d)
29 years
If \(\frac{3p+2}{5}-\frac{4p-3}{7}+\frac{p-1}{35}=4.\) find the value of p.
- (a)
65
- (b)
63
- (c)
36
- (d)
56
The sum of five times a number and 13 is 48. What is the number?
- (a)
3
- (b)
5
- (c)
7
- (d)
9
Guru is 20 years older than his son. If the sum of their ages is 50 years, how old is his son?
- (a)
5 years
- (b)
10 years
- (c)
15 years
- (d)
20 years
If \(c=\frac{5}{9}(F-32)\) what is the value F?
- (a)
\(\frac{5C}{9}-32\)
- (b)
\(\frac{9C}{5}-32\)
- (c)
\(\frac{9C}{5}+32\)
- (d)
\(\frac{5C}{9}+32\)
The sum of two-thirds of a number and one-fifth of the same number is 13. Find the number.
- (a)
15
- (b)
3
- (c)
13
- (d)
5
The denominator of a fraction is 3 more than its numerator. If 2 is added to both the numerator and the denominator, the new fraction is equivalent to \(\frac{2}{3}\) What is the original fraction?
- (a)
\(\frac{3}{7}\)
- (b)
\(\frac{4}{7}\)
- (c)
\(\frac{2}{3}\)
- (d)
\(\frac{3}{5}\)
144 beads were shared equally among some children. If there were 3 children fewer, each child would have 16 beads each. How many children were there?
- (a)
8
- (b)
9
- (c)
12
- (d)
11
You are decorating a gift pack with 15 flowers. You want an equal number of flowers in each of the 3 rows on the gift pack. Which equation would you use to find the number of flowers, r, in each row?
- (a)
r + 3 = 15
- (b)
15 + r = 3
- (c)
3r = 15
- (d)
\(\frac { 3 }{ r } =15\)
If \(\frac { 2x }{ 1+\frac { 1 }{ 1+\frac { x }{ 1-x } } } =1\) , then find the value of x.
- (a)
1
- (b)
4/3
- (c)
1/3
- (d)
2/3
What is the value of p that makes the following expression true?
p-{-4-(2-8\(\div \)4)} = 8
- (a)
-12
- (b)
-4
- (c)
4
- (d)
12
A shopkeeper sells bananas in two types of boxes, one small and one large. A large box contains as many as 6 small boxes plus 2 loose bananas. Form an equation which gives the number of bananas in each small box, if the number of bananas in 1 large box is 50.
- (a)
3x + 1 = 50
- (b)
x + 1 = 20
- (c)
6x + 2 = 50
- (d)
2x + 1 = 20
The teacher tells the class that the highest marks obtained by a student in her class is four times the lowest marks plus 6. The highest score is 65. Form the equation which will calculate the lowest marks.
- (a)
6m + 4 = 65
- (b)
4m + 65 = 6
- (c)
4m + 6 = 65
- (d)
6m + 65 = 4
There are some lotus flowers in a pond and some bees are hovering around. If one bee lands on each flower, one bee will be left . If two bees land on each flower, one flower will be left. Then, the number of flowers and bees respectively are ____________
- (a)
3, 4
- (b)
4, 3
- (c)
2, 3
- (d)
3, 2
A number consists of two digits whose sum is 9. If 27 is added to the number, its digits are interchanged. Which of the given steps is CORRECT to find the number?
Step 1 : Let the unit's digit be x.
Step 2 : Then, ten's digit = (9 - x)
\(\therefore\) Number = 10 \(\times\) (9 - x) + x
\(\Rightarrow\) 90 - 10x + x = (90 - 9x)
Step 3 : Adding 27 to the number 90 - 9x, we get 117 - 9x.
Step 4 : Number with digits interchanged is 10x + (9 - x) = 9x + 9.
Step 5 :117 - 9x = 9x + 9.
Step 6 : Therefore unit's digit = 6 and ten's digit = 3.
Step 7 : Hence the number = 36.
- (a)
Only Step 4
- (b)
Both Step 1 and Step 2
- (c)
Step 1, 2, 3 and 4
- (d)
All steps are correct
Match the following.
(i) Arjun's father's age is 5 years more than four times Arjun's age. Find Arjun's age, if his father is 37 years old. | (p) 9 |
(ii) Ramesh says that he has 8 notebooks more than four times the number of notebooks Anuj has. Ramesh has 48 notebooks. How many notebooks does Anuj have? | (q) 8 |
(iii) Varun says that he has 11 erasers more than five times the number of erasers Sameer has. Varun has 56 erasers. How many erasers does Sameer have? | (r) 10 |
- (a)
(i) \(\rightarrow\) (q), (ii) \(\rightarrow\) (p), (iii) \(\rightarrow\) (r)
- (b)
(i) \(\rightarrow\) (q), (ii) \(\rightarrow\) (r), (iii) \(\rightarrow\) (p)
- (c)
(i) \(\rightarrow\) (p), (ii) \(\rightarrow\) (q), (iii) \(\rightarrow\) (r)
- (d)
(i) \(\rightarrow\) (p), (ii) \(\rightarrow\) (r), (iii) \(\rightarrow\) (q)