Solved Examples

1. 45 of a number exceeds its 23 by 8. The number is 
a. 30
b. 60
c. 90
d. None of these
Correct Option : B
Explanation:
Let the number be 'a'.
45a−23a=8
⇒12a−10a15=8
⇒2a=120⇒a=60

2. If 1 is added to the denominator of fraction, the fraction becomes 12.  If 1 is added to the numerator, the fraction becomes 1.  The fraction is 
a. 47
b. 59
c. 23
d. 1011
Correct Option: C
Explanation:
Let the required fraction be ab. Then
⇒ab+1=12⇒2a–b=1 ---- (1)
⇒a+1b=1  ⇒a–b=–1 ------- (2)
Solving (1) & (2) we get a = 2, b=3
Fraction = ab=23

3. The sum of two numbers is twice their difference.  If one of the numbers is 10, the other number is
a. 313
b. 30
c. −313
d. a or b
Correct Option:  D
Explanation:
Let the other number be a. 
Given that, 10+a=2(a−10)⇒a=30
or if the other number is less than 10, 10+a=2(10−a)⇒a=103=313

4. The sum of squares of two numbers is 80 and the square of their difference is 36.  The product of the two numbers is.
a. 22
b. 44
c. 58
d. 116
Correct Option: A
Explanation :
Let the numbers be x and y . Then
x2+y2=80 and (x−y)2=36
(x−y)2=36⇒x2+y2−2xy=36
⇒2xy=(x2+y2)−36=80−36=44
⇒xy=22

5. 11 times a number gives 132.  The number is 
a. 11
b. 12
c. 13.2
d. None
Correct Option: B
Explanation:
Let the number be 'N'
11×N=132⇒N=12

6. If 1/5th of a number decreased by 5 is 5, then the number is 
a. 25
b. 50
c. 60
d. 75
Correct Option: B
Explanation :
Let the number be a, then
a5−5=5⇒a5=10⇒a=50

7. The difference of two numbers is 2 and the difference of their squares is 12.  The sum of the number is 
a. 6
b. 8
c. 10
d. 22
Correct Option: A
Explanation:
Let the numbers be a, b; ⇒ a-b=2 and
a2−b2=12
a+b=a2−b2a−b=122=6

8. The sum of two numbers is 29 and the difference of their squares is 145.  The difference between the number is
a. 13
b. 5
c. 8
d. 11
Correct Option: B
Explanation:
Let the numbers be x and y, then
(x−y)=x2−y2(x+y)
=14529=5

9. The difference between the squares of two consecutive numbers is 35.  The numbers are
a. 14,15
b. 15,16
c. 17,18
d. 18,19
Correct Option: C
Explanation:
Let the numbers be a and (a+1)
(a+1)2−a2=35
⇒a2+2a+1−a2=35
⇒2a=34 or a = 17
The numbers are 17 & 18.

10.3th4of1th5 of a number is 60.  The number is 
a. 300
b. 400
c. 450
d. 1200
Correct Option: B
Explanation:
Let the number be N. Then
34×15×N=60⇒3N=1200⇒N=400