QUANTITATIVE APTITUDE
Quantitative aptitude material on problems on numbers for bank exams
SIMPLE PROBLEMS ON NUMBERS
QUESTIONS
EG:
(1/3) OF (2/5) OF A NUMBER IS 24 THEN FIND THAT NUMBER?
(1/3)* (2/5) *X = 24
X = (24 *3*5)/2
= 180
EG:
IF x2 = 25 FIND X?
x2-25 = 0
(X+5)(X-5)
X=-5 OR X= +5
EG :
IF (1/6)TH OF (3/7) OF A NUMBER IS 21 WHAT IS 30% OF THAT NUMBER?
(1/6)*(3/7)*X = 21
X = (21*6*7)/3
= 88.2
EG:
WHEN 14 IS ADDED TO A NUMBER IT BECOMES (5/4) TH OF ORIGINAL NUMBER WHAT
IS 25% OF THAT NUMBER?
X+14 = (5/4) X
4X+56 = 5X
X = 56
25% of (56)
14
EG:
A NUMBER CAN DIVIDED BY 4 THEN IT REDUCED BY 21 FIND THE NUMBER?
X REDUCED BY MEAN X-21
(X-(X/4)) = 21
3X/4 = 21
X = 28
EG:
A NUMBER WHEN DIVIDED BY 4 IT REDUCED TO 21 FIND THAT NUMBER?
X/4 = 21
X = 84
EG:
A NUMBER EXCEEDS 20% OF ITSELF BY 40 FIND THAT NUMBER?
X-(20%)X = 40
X-(X/5) = 40
4X = 200
X= 50
EG:
A NUMBER IS 68% OF OTHER NUMBER IF THE SUM OF THOSE TWO NUMBERS IS 84% OF 500 FIND THE
LARGER NUMBER?
100%X + 68%X= 84%OF 500
X =250
EG:
THE SUM OF 3 CONSICUTIVE EVEN NUMBERS IS 108 WHAT WILL BE THE MIBBLE NUMBER?
X+X+2+X+4 = 108
3X+6 = 108
3x = 108
34
MIDDLE NUMBER = 34+2 = 36
EG:
THE SUM OF 3 CONSICUTIVE NUMBERS IS 27 WHAT IS SQUARE OF MIDDLE NUMBER?
X+X+1+X+2 = 27
MIDDLE NUMBER = X SQUARE
EG:
RAMU WAS ASKED TO DIVIDE A NUMBER BY 5 BUT WRONGLY MULTIPLIED THE NUMBER WITH 5 HIS ANSWER IS 144
MORE THAN THE CORRECT ANSWER WHAT WAS CORRECT NUMBER?
X
(X/5) 5X
(5X-(X/5)) = 144
X = 30
X/5 =30/5 = 6
EG:
A NUMBER WHEN MULTIPLIED BY 17 IT INCREASED BY 96 FIND THAT NUMBER?
X(17) = X+96
16X = 96
X =6
EX:
WHEN 84 IS ADDED TO A NUMBER THE NEW NUMBER BECOMES 400% OF ORIGINAL NUMBER?
X+84 = X(400/100)
3X = 84
X = 28
EG:
A NUMBER IS AS MUCH GREATERTHAN 65 AS IS LESSTHAN 105 FIND THAT NUMBER?
65< X < 105
85
X-65 = 105=X
2X = 170
X =85
EG:
3 NUMBERS ARE IN THE RATIO 4 : 5 :6 AND THE AVERAGE IS 25 FIND THE NUMBER?
(4X+5X+6X)/3 = 25
15X = 25*3
X = 5
4 5 6
(5*5) (6*5)
EG:
2 NUMBERS ARE SUCHTTHAT THE RATIO BETWEEN 4:7 IF EACH NUMBER INCREASED BY 4 THE RATIO BECOMES 3:5 FIND THE LARGER NUMBER?
4X+4 = 3
....... ...
7X+4 5
20X+20 = 21X+12
X = 8
7X = 7*8 = 56
EG :
THE SUM OF TWO NUMBERS IS 22 FIVE TIMES OF ONE NUMBER IS 6 TIMES OF OTHER NUMBER FIND THAT NUMBER?
5X = 6Y
X/Y = 6/5
X= 6Y/5
(6Y/5) + Y = 22
Y = 10
X =12
THE SUM OF THREE NUMBERS IS 264 IF THE FIRST NUMBER IS TWICE THE SECOND AND THIRD NUMBER IS 1/3RD OF FIRST
FIND THE NUMBER?
2X+X+(2X)(1/3) = 264
3X+ (2X/3) = 264
9X +2X = 264 *3
11X = 264 *3
X = 72
2ND METHOD:
X : Y : Z
6 : 3 : 2
11P = 264
P = 72
EG:
IF THE NUMANATOR AND DENOMINATOR ARE INCREASED BY 20% AND 30% RESPECTIVILY THE FRACTION BECOMES 9/13 WHAT WAS THE ORIGINAL FRACTION?
(100X +20x) = 9
............. ...
(100Y+30X) 13
12X/13Y = 9/13
X/Y = 9/12
EG:
IF 20% OF THE NUMANATOR AND 30% OF THE DENOMINATOR IS TAKEN THEN NEW FRACTION BECOMES 7/9 FIND THE ORIGINAL
FRACTION?
(20%X)/(30%Y) = (7/9)
(2X/3Y) = (7/9)
X/Y =(7/9)(3/2)
X = 7
..... ....
Y 6
EG:
IN A 2 DIGIT NUMBER THE DIGITS IN UNIT PRICE IS TWO TIMES MORE THAN THREE OF DIGIT IN THE TENS PLACE IF THE SUM OF TWO DIGITS IS 6 FIND THE NUMBER?
Y = 2+3X
X+3X+2 = 6
4X =4
X = 1
Y = 6-1 = 5
15
COMPLEX PROBLEMS ON NUMBERS QUESTIONS :
EG:
THE SUM OF THE DIGITS OF A TWO DIGIT NUMBER IS 8 IF THE DIGITS ARE REVERSED THE NUMBER IS DECREASED BY 54 FIND THE NUMBER?
X+Y = 8
TWO DIGTI NUMBER = 10X+Y 10Y +X
(10X+Y) - (10Y-X) = 54
9X - 9Y = 54
X-Y = 6
X +Y = 8
EG:
THE DIFFERENCE BETWEEN TWO DIGIT NUMBER AND THE NUMBER OBTAINED AFTER INTERCHANGING 2 DIGITS IS 27
IF THE SUM OF THE TWO DIGITS IS 15 WHAT IS THE TWO DIGIT NUMBER?
ORIGINAL = 10X+Y
REVERSE = 10y+X
(10X+Y)-(10Y-X) = 27
(10Y+X)-(10X+Y) = 27
X-Y = 3
X+Y = 15
X = 96 OR 69
EG:
THE DIFFERENCE NBETWEEN THE TWO DIGTI NUMBER AND THE NUMBER OBTAINED BY INTERCHANGING THE TWO
DIGIT IS 18 THE SUM OF THE TWO DIGITS OF A NUMBER IS 12 WHAT IS THE PRODUCT OF THE DIGITS OF TWO DIGIT NUMBER?
(X-Y) OR (X+Y) = 18/9 =2
X+Y = 12
X-Y = 2
2X = 14
X =7
7-2 =5
PRODUCT = 5*7 = 35
EG:
THE SUM OF THE SQUARES OF TWO DIGIT IS 80 AND THE SQUARE OF DIFFERENCE IS 36 FIND THE PRODUCT OF TWO NUMBERS?
(X-Y)(X-Y) = 36
x^2 +y^2 = 80
80-2XY = 36
XY = 22
EG:
THE DIFFERENCE OF TWO NUMBERS IS 5 AND THE DIFFERENCE OF SQUARE IS 135 FIND THE SUM OF THE SUMBERS?
X-Y = 5
x^2-y^2= 135
(X+Y)(X-Y) = 135
135/5
27
X+Y = 27
........ ...
X-Y 5
X = 32
EG:
THE SUM OF TWO NUMBERS IS 29 AND THE DIFFERENCE OF THE SQUARE IS 145 FIND THE DIFFERENCE BETWEEN THE NUMBERS?
X+Y = 29
x^2 -y^2 = 145
(X+Y)(X-y) = 145
(X-Y) = 145/29 = 5
EG:
A NUMBER WHEN INCREASED BY 20% GIVES 720 FIND THE NUMBER?
100X + 20X = 720
120X = 720
X = 6
100X = 600
EG:
WHEN 60 IS ADDED TO 60% OF A NUMBER THE RESULT IS THE NUMBER ITSELF FIND THE NUMBER?
60+(60%X) = 100%X
40%X = 60
X =150
EG:
WHEN 75 IS ADDED TO 75% OF A NUMBER THE RESULT IS 125% OF THAT ORIGINAL NUMBER?
75 +75%X = 125%X
75 = 50%X
100%X = 150
EG:
THE PRODUCT OF TWO NUMBERS IS 120
THE SUM OF THEIR SQUARE IS 289
FIND THE SUM OF THE TWO NUMBERS?
XY - 120
x^2 +y^2 =289
x^2 +y^2+2XY = 289 +2XY
x^2 +y^2 = 289+2*120
x^2 +y^2 = 529
X-Y = 7
X+Y =23
X= 15 Y = 8
EG:
THERE ARE TWO NUMBERS SUCHTHAT THE SUM OF TWICE THE FIRST AND THRICE THE SECOND IS 39 BY THE SUM OF THRICE THE FIRST AND TWICE THE SECOND IS 36 FIND THE
LARGER OF THE TWO NUMBERS?
3Y+2X = 39
2Y+3X = 36
X = 6
Y =9
EG:
SHANKAR GETS 3 MARKS IN EXAMINATION FOR EACH CORRECT ANSWER 2 MARKS FOR EACH WRONG ANSWER HE ATTEMPTS ALL THE 30 QUESTIONS AND SCORED 40 MARKS FIND THE NUMBER
OF HIS CORRECT ANSWERS?
NO OF QUESTIONS EQUATON = X+Y = 30
3X-2Y = 40
2(X+Y) = 30*2
X =100/5 =20
