Problems on Numbers

1. 24 is divided into two parts such that 7 times the first part added to 5 times the second part gives 146. The first part is 
a. 11
b. 13
c. 16
d. 17
Correct Option: B
Explanation:
Let the first and second parts be a and 24  a, then
7a+5(24−a)=146
⇒7a+120−5a=146
⇒2a=26 or a = 13

2. The product of two numbers is 120.  The sum of their squares is 289.  The sum of the two numbers is :
a. 20
b. 23
c. 169
d. None
Correct Option: B
Explanation:
Let the number be x and y . Then
(x+y)2=(x2+y2)+2xy=289+2x120
=289+240=529⇒x+y=529−−−√=23

3. The sum of squares of two numbers is 68 and the square of their difference is 36.  The product of the two numbers is 
a. 16
b. 32
c. 58
d. 104
Correct Option:a
Explanation:
Let the numbers be x and y. Then
x2+y2=68&(x−y)2=36
But (x−y)2=36⇒x2+y2−2xy=36
⇒68−2xy=36⇒2xy=32
⇒xy=16

4. The sum of seven numbers is 235.  The average of the first three is 23 and that of the last three is 42.  The fourth number is 
a. 40
b. 126
c. 69
d. 195
Correct Option: A
Explanation:
(23×3+a+42×3)=235⇒a=40

5. Two numbers are such that the ratio between them is 3:5 but if each is increased by 10, the ratio between them becomes 5 : 7, the numbers are
a. 3, 5
b. 7, 9
c. 13, 22
d. 15, 25
Correct Option: D
Explanation:
Let the numbers be 3a and 5a
Then 3a+105a+10=57
⇒7(3a+10)=5(5a+10)⇒a=5
The numbers are 15 & 25

6.  A fraction becomes 4 when 1 is added to both the numerator and denominator, and it becomes 7 when 1 is subtracted from both the numerator and denominator.  The numerator of the given fraction is :
a. 2
b. 3
c. 7
d. 15
Correct Option: D
Explanation:
Let the required fraction be ab
Then a+1b+1=4⇒a−4b=3
and a−1b−1=7⇒a−7b=−6
Solving these equations we get,
a=15
b=3

7. A number exceeds 20% of itself by 40.  The number is
a. 50
b. 60
c. 80
d. 320
Correct Option: A
Explanation:
Let the answer be 'a'
Then a−20100a=40⇒5a−a=200
⇒a=50

8. Three numbers are in the ratio 3:4:5.  The sum of the largest and the smallest equals the sum of the third and 52.The smallest number is :
a. 20
b. 27
c. 39
d. 52
Correct Option: C
Explanation:
Let the numbers be 3 N, 4 N and 5 N
Then 5N+3N = 4 N +52
⇒4N=52⇒N=13
The smallest number =3N=3 x 13=39

9. If 16% of 40% of a number is 8, then the number is 
a. 200
b. 225
c. 125
d. 320
Correct Option: C
Explanation:
Let 16100×40100×a=8

a = 8×100×10016×40=125

10. If 3 is added to the denominator of a fraction, it becomes 13 and if 4 be added to its numerator, it becomes 34 ; the fraction is :
a. 49
b. 320
c. 724
d. 512
Correct Option: D
Explanation:
Let the required fraction be ab
Then ab+3=13
⇒3a−b=3 and
a+4b=34⇒4a−3b=−16 solving,we get
a=5, b=12; required answer = 5/12