Q 1 Mathematics Finding The Number
A number is as much greater than 36 as is less than 86. Find the number?
View answer & explanation Ans: 61
Correct Answer: 61
The number lies midway between 36 and 86, so it is (36 + 86) / 2 = 61.
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Arithmetic: Problems on Numbers — Solved MCQs Solved MCQs
Solved problems on numbers MCQs — 48 questions on linear and quadratic equations, two-digit numbers, consecutive numbers, ratios and fractions with verified answers and explanations. Free online practice for FPSC, PPSC, NTS and all one-paper exams. Covers number equations, reciprocals, digit problems and ratio problems.
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Questions
48
Time
48
Minutes
Subjects
1
Topics
32
Read mode shows correct answers. Attempt mode hides answers, starts timer, and shows your result after submission.
About this paper
This is the Arithmetic: Problems on Numbers solved MCQ bank from Advanced FPSC & Other Federal Model Papers (Edition 32): 48 published questions (book pp. 742-746) on finding unknown numbers, two-digit and consecutive numbers, ratios, fractions and reciprocal equations, each with a worked explanation and an answer checked against the book's printed key. The book prints 50 items; 2 are dropped rather than guessed because no unique correct option exists as printed (Q16 states an operation but no result, and Q43's correct greater fraction 7/6 is not among the options), and the printed key agrees with every published answer.
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Arithmetic: Problems on Numbers — Solved MCQs
Read mode 48 MCQs · 48 minutes
Subject 1
Mathematics
1
Topic Section
Finding The Number
1 solved MCQs shown directly below
2
Topic Section
Linear Equation
4 solved MCQs shown directly below
Q 2 Mathematics Linear Equation
Find a number such that when 15 is subtracted from 7 times the number, the result is 10 more than twice the number.
View answer & explanation Ans: 5
Correct Answer: 5
7x - 15 = 2x + 10 gives 5x = 25, so x = 5.
Q 10 Mathematics Linear Equation
If a number is decreased by 4 and divided by 6, the result is 8. What would be the result if 2 is subtracted from the number and then it is divided by 5?
View answer & explanation Ans: 10
Correct Answer: 10
The number is 6 x 8 + 4 = 52, and (52 - 2) / 5 = 10.
Q 12 Mathematics Linear Equation
A number is doubled and 9 is added. If the result is trebled, it becomes 75. What is that number?
View answer & explanation Ans: 8
Correct Answer: 8
3(2x + 9) = 75 gives 2x + 9 = 25, so x = 8.
Q 20 Mathematics Linear Equation
If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is:
View answer & explanation Ans: 4
Correct Answer: 4
2x + 20 = 8x - 4 gives 6x = 24, so x = 4.
3
Topic Section
Two Numbers With Fractions
1 solved MCQs shown directly below
Q 3 Mathematics Two Numbers With Fractions
The sum of two numbers is 184. If one-third of the one exceeds one-seventh of the other by 8, find the smaller number:
View answer & explanation Ans: 72
Correct Answer: 72
With the numbers x and 184 - x, x/3 - (184 - x)/7 = 8 gives x = 72, and 72 is the smaller of 72 and 112.
4
Topic Section
Sum And Product
1 solved MCQs shown directly below
Q 4 Mathematics Sum And Product
If the sum of two numbers is 42 and their product is 437, then find the absolute difference between the number:
View answer & explanation Ans: 4
Correct Answer: 4
The difference squared is 42 squared minus 4 times 437, which is 16, so the absolute difference is 4.
5
Topic Section
Consecutive Even Numbers And Average
1 solved MCQs shown directly below
Q 5 Mathematics Consecutive Even Numbers And Average
The average of four consecutive even numbers is 27. Find the largest of these numbers:
View answer & explanation Ans: 30
Correct Answer: 30
Four consecutive even numbers averaging 27 are 24, 26, 28 and 30, so the largest is 30.
6
Topic Section
Two Digit Number And Digit Sum
1 solved MCQs shown directly below
Q 6 Mathematics Two Digit Number And Digit Sum
The ratio between a two-digit number and the sum of the digits of that number is 4:1. If the digit is in the unit's place is 3 more than the digit in the ten's place, what is the number?
View answer & explanation Ans: 36
Correct Answer: 36
The number 36 has digit sum 9, and 36 is 4 times 9, while its unit digit 6 is 3 more than its ten digit 3.
7
Topic Section
Two Digit Number, Digits Interchanged
1 solved MCQs shown directly below
Q 7 Mathematics Two Digit Number, Digits Interchanged
A number consists of two digits. The sum of the digits is 9. If 63 is subtracted from the number, its digits are interchanged. Find the number:
View answer & explanation Ans: 81
Correct Answer: 81
Subtracting 63 from 81 gives 18, the digits interchanged, and 8 + 1 = 9.
8
Topic Section
Reciprocals
1 solved MCQs shown directly below
Q 8 Mathematics Reciprocals
50 is divided into two parts such that the sum of their reciprocals is 1/12. Find the two parts:
View answer & explanation Ans: 20 and 30
Correct Answer: 20 and 30
Parts x and 50 - x with 1/x + 1/(50 - x) = 1/12 give x(50 - x) = 600, so the parts are 20 and 30.
9
Topic Section
Fraction Of A Number
4 solved MCQs shown directly below
Q 9 Mathematics Fraction Of A Number
The difference between a number and its three-fifth is 50. What is the number?
View answer & explanation Ans: 125
Correct Answer: 125
The number minus its three-fifth is two-fifth of the number, so 2x/5 = 50 gives x = 125.
Q 11 Mathematics Fraction Of A Number
If one-third of one-fourth of that number is 15, then three tenth of that number is:
View answer & explanation Ans: 54
Correct Answer: 54
One-third of one-fourth of the number is 15, so the number is 180, and three-tenth of 180 is 54.
Q 13 Mathematics Fraction Of A Number
Three-fourth of a number is 60 more than its one-third. The number is:
View answer & explanation Ans: 144
Correct Answer: 144
Three-fourth minus one-third of the number is 5/12 of it, so 5x/12 = 60 gives x = 144.
Q 14 Mathematics Fraction Of A Number
When 24 is subtracted from a number, it reduces to its four-seventh. What is the sum of the digits of that number?
View answer & explanation Ans: 11
Correct Answer: 11
x - 24 = 4x/7 gives x = 56, and the sum of its digits is 5 + 6 = 11.
10
Topic Section
Number Increased On Multiplication
1 solved MCQs shown directly below
Q 15 Mathematics Number Increased On Multiplication
Find the number which when multiplied by 15 is increased by 196.
View answer & explanation Ans: 14
Correct Answer: 14
15x - x = 196 gives 14x = 196, so x = 14.
11
Topic Section
Fractional Parts Equation
3 solved MCQs shown directly below
Q 16 Mathematics Fractional Parts Equation
A number whose fifth part increased by 4 is equal to its fourth part diminished by 10, is:
View answer & explanation Ans: 280
Correct Answer: 280
x/5 + 4 = x/4 - 10 gives x/20 = 14, so x = 280.
Q 19 Mathematics Fractional Parts Equation
If the sum of one-half and one fifth of a number exceeds one third of that number by 7 1/3, the number is:
View answer & explanation Ans: 20
Correct Answer: 20
(1/2 + 1/5 - 1/3) of the number is 11x/30, and 11x/30 = 22/3 gives x = 20.
Q 21 Mathematics Fractional Parts Equation
If 50 is subtracted from two-third of a number, the result is equal to sum of 40 and one-fourth of that number. What is the number?
View answer & explanation Ans: 216
Correct Answer: 216
2x/3 - 50 = 40 + x/4 gives 5x/12 = 90, so x = 216.
12
Topic Section
Percentage Difference
1 solved MCQs shown directly below
Q 17 Mathematics Percentage Difference
The difference of two numbers is 20% of the larger number. If the smaller number is 12, the larger one is:
View answer & explanation Ans: 15
Correct Answer: 15
The larger number minus 12 is 20% of the larger number, so 80% of it is 12 and it equals 15.
13
Topic Section
Fractional Parts Difference
1 solved MCQs shown directly below
Q 18 Mathematics Fractional Parts Difference
If one-seventh of a number exceeds its eleventh part by 100, then the number is:
View answer & explanation Ans: 1925
Correct Answer: 1925
x/7 - x/11 = 100 gives 4x/77 = 100, so x = 1925.
14
Topic Section
Number And Its Square
1 solved MCQs shown directly below
Q 22 Mathematics Number And Its Square
If the sum of a number and its square is 182, what is the number?
View answer & explanation Ans: 13
Correct Answer: 13
x squared plus x equals 182, and 13 squared plus 13 is 182.
15
Topic Section
Quadratic Equation
2 solved MCQs shown directly below
Q 23 Mathematics Quadratic Equation
Twenty times a positive integer is less than its square by 96, what is the integer?
View answer & explanation Ans: 24
Correct Answer: 24
x squared minus 20x equals 96, and 24 squared minus 20 times 24 is 96.
Q 24 Mathematics Quadratic Equation
Thrice the square of a natural number decreased by 4 times, the number is equal to 50 more than the number. The number is:
View answer & explanation Ans: 5
Correct Answer: 5
3x squared minus 4x equals x + 50, giving 3x squared minus 5x minus 50 = 0, whose natural-number root is 5.
16
Topic Section
Reciprocal Equation
5 solved MCQs shown directly below
Q 25 Mathematics Reciprocal Equation
The sum of a number and its reciprocal is one eighth of 34. What is the product of the number and its square root?
View answer & explanation Ans: 8
Correct Answer: 8
x + 1/x = 34/8 gives the root x = 4, and the product of 4 and its square root 2 is 8.
Q 26 Mathematics Reciprocal Equation
Two third of a positive number and 25/216 of its reciprocal are equal. The number is:
View answer & explanation Ans: 5/12
Correct Answer: 5/12
(2/3)x = (25/216)(1/x) gives x squared = 25/144, so the positive number is 5/12.
Q 27 Mathematics Reciprocal Equation
Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.
View answer & explanation Ans: 3
Correct Answer: 3
x + 17 = 60/x gives x squared + 17x - 60 = 0, whose positive root is 3.
Q 28 Mathematics Reciprocal Equation
A positive number when decreased by 4 is equal to 21 times the reciprocal of the number. The number is:
View answer & explanation Ans: 7
Correct Answer: 7
x - 4 = 21/x gives x squared - 4x - 21 = 0, whose positive root is 7.
Q 29 Mathematics Reciprocal Equation
The sum of a positive number and its reciprocal is thrice the difference of the number and its reciprocal. The number is:
View answer & explanation Ans: √2
Correct Answer: √2
x + 1/x = 3(x - 1/x) gives 4/x = 2x, so x squared = 2 and x = √2.
17
Topic Section
Ratio And Average
1 solved MCQs shown directly below
Q 30 Mathematics Ratio And Average
Three numbers are in the ratio 4 : 5 : 6 and their average is 25. The largest number is:
View answer & explanation Ans: 30
Correct Answer: 30
Numbers in the ratio 4:5:6 averaging 25 sum to 75, so one part is 5 and the largest is 6 x 5 = 30.
18
Topic Section
Ratio Of Three Numbers
2 solved MCQs shown directly below
Q 31 Mathematics Ratio Of Three Numbers
The sum of three numbers is 264. If the first number be twice the second and third number be one-third of the first, then the second number is:
View answer & explanation Ans: 72
Correct Answer: 72
With the second number x, the numbers are 2x, x and 2x/3, summing to 11x/3 = 264, so x = 72.
Q 47 Mathematics Ratio Of Three Numbers
The sum of three numbers is 136. If the ratio between first and second be 2:3 and that between second and third is 5:3, then the second number is:
View answer & explanation Ans: 60
Correct Answer: 60
First, second and third numbers in the ratio 10:15:9 sum to 136, so one part is 4 and the second number is 15 x 4 = 60.
19
Topic Section
Two Numbers And Ratio
1 solved MCQs shown directly below
Q 32 Mathematics Two Numbers And Ratio
The sum of two numbers is 22. Five times one number is equal to 6 times the other. The bigger of the two numbers is:
View answer & explanation Ans: 12
Correct Answer: 12
Five times one number equals six times the other and they sum to 22, so the numbers are 12 and 10 and the bigger is 12.
20
Topic Section
Sum And Difference
2 solved MCQs shown directly below
Q 33 Mathematics Sum And Difference
The sum of two numbers is 25 and their difference is 13. Find their product.
View answer & explanation Ans: 114
Correct Answer: 114
The numbers summing to 25 with difference 13 are 19 and 6, and their product is 114.
Q 34 Mathematics Sum And Difference
If the sum of two numbers is 33 and their difference is 15, the smaller number is:
View answer & explanation Ans: 9
Correct Answer: 9
The smaller number is (33 - 15) / 2 = 9.
21
Topic Section
Difference And Product
2 solved MCQs shown directly below
Q 35 Mathematics Difference And Product
The difference between two integers is 5. Their product is 500. Find the numbers:
View answer & explanation Ans: 20, 25
Correct Answer: 20, 25
The integers 20 and 25 differ by 5 and their product is 500.
Q 36 Mathematics Difference And Product
Two numbers differs by 5. If their product is 336, then the sum of the two numbers is:
View answer & explanation Ans: 37
Correct Answer: 37
The positive pair differing by 5 with product 336 is 16 and 21, whose sum is 37.
22
Topic Section
Difference Of Squares
1 solved MCQs shown directly below
Q 37 Mathematics Difference Of Squares
If the difference of two numbers is 3 and the difference of their squares is 39, then the larger number is:
View answer & explanation Ans: 8
Correct Answer: 8
The difference of squares is (a - b)(a + b) = 3(a + b) = 39, so a + b = 13 and the larger number is (13 + 3) / 2 = 8.
23
Topic Section
Consecutive Numbers
1 solved MCQs shown directly below
Q 38 Mathematics Consecutive Numbers
The sum of three consecutive numbers is 87. The greatest among three number is:
View answer & explanation Ans: 30
Correct Answer: 30
Three consecutive numbers summing to 87 are 28, 29 and 30, so the greatest is 30.
24
Topic Section
Consecutive Even Numbers
1 solved MCQs shown directly below
Q 39 Mathematics Consecutive Even Numbers
What is the sum of two consecutive even numbers, the difference of whose squares is 84?
View answer & explanation Ans: 42
Correct Answer: 42
Consecutive even numbers x and x + 2 with (x + 2) squared minus x squared = 84 give x = 20, so the numbers are 20 and 22 and their sum is 42.
25
Topic Section
Consecutive Numbers And Squares
1 solved MCQs shown directly below
Q 40 Mathematics Consecutive Numbers And Squares
The sum of the squares of three consecutive natural numbers is 2030. What is the middle number?
View answer & explanation Ans: 26
Correct Answer: 26
(n - 1) squared + n squared + (n + 1) squared = 3n squared + 2 = 2030 gives n squared = 676, so the middle number is 26.
26
Topic Section
Two Digit Number And Digits
1 solved MCQs shown directly below
Q 41 Mathematics Two Digit Number And Digits
A two-digit number exceeds the sum of the digits of that number by 18. If the digit at the unit's place is double the digit in the ten's place, what is the number?
View answer & explanation Ans: 24
Correct Answer: 24
With ten digit t and unit digit 2t, the number 12t exceeds the digit sum 3t by 9t = 18, so t = 2 and the number is 24.
27
Topic Section
Fractions And Product
1 solved MCQs shown directly below
Q 42 Mathematics Fractions And Product
In a pair of fractions, fraction A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?
View answer & explanation Ans: 2/5
Correct Answer: 2/5
Fraction A is twice fraction B and their product is 2/25, so 2B squared = 2/25 gives B = 1/5 and A = 2/5.
28
Topic Section
Fraction From Numerator Denominator Sum
1 solved MCQs shown directly below
Q 43 Mathematics Fraction From Numerator Denominator Sum
The sum of the numerator and denominator of a fraction is 11. If 1 is added to the numerator and 2 is subtracted from the denominator, it becomes 2/3. The fraction is:
View answer & explanation Ans: 3/8
Correct Answer: 3/8
With numerator n and denominator 11 - n, (n + 1)/(9 - n) = 2/3 gives n = 3, so the fraction is 3/8.
29
Topic Section
Fraction From Numerator Denominator Relation
1 solved MCQs shown directly below
Q 44 Mathematics Fraction From Numerator Denominator Relation
The denominator of a fraction is 3 more than the numerator. If the numerator as well as the denominator is increased by 4, the fraction becomes 4/5. What was the original fraction?
View answer & explanation Ans: 8/11
Correct Answer: 8/11
With numerator n and denominator n + 3, (n + 4)/(n + 7) = 4/5 gives n = 8, so the original fraction is 8/11.
30
Topic Section
Fraction And Denominator Change
1 solved MCQs shown directly below
Q 45 Mathematics Fraction And Denominator Change
The difference between the numerator and the denominator of a fraction is 5. If 5 is added to its denominator, the fraction is decreased by 1 1/4. Find the value of the fraction:
View answer & explanation Ans: 2 1/4
Correct Answer: 2 1/4
Taking the numerator to exceed the denominator by 5, n = d + 5 and n/d - n/(d + 5) = 5/4 give d = 4 and n = 9, so the fraction is 9/4, that is 2 1/4.
31
Topic Section
Fraction And Denominator
1 solved MCQs shown directly below
Q 46 Mathematics Fraction And Denominator
When the numerator of a fraction increases by 4, the fraction increases by 2/3. The denominator of the fraction is:
View answer & explanation Ans: 6
Correct Answer: 6
Increasing the numerator by 4 increases the fraction by 4/d, so 4/d = 2/3 gives d = 6.
32
Topic Section
System Of Three Numbers
1 solved MCQs shown directly below
Q 48 Mathematics System Of Three Numbers
If the three numbers, the sum of the first two is 45; the sum of the second and the third is 55 and the sum of the third and thrice first is 90. The third number is:
View answer & explanation Ans: 30
Correct Answer: 30
From a + b = 45, b + c = 55 and c + 3a = 90, a = 20 and c = 30.
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Paper practice FAQs
How many questions are in the Arithmetic: Problems on Numbers MCQ bank? +
48 questions are published. The book prints 50 items; 2 are dropped because no unique correct option exists as printed, rather than guessed.
What does the Arithmetic: Problems on Numbers bank cover? +
Finding unknown numbers from linear, fractional and quadratic equations, two-digit numbers and digit sums, consecutive and consecutive even numbers, ratios of two and three numbers, fractions and their reciprocals.
Are the answers verified? +
Yes. Every published answer was recomputed from scratch and checked against the book's printed Answer Key on pages 745-746; the key agrees with all 48 published answers, and the 2 dropped items are recorded in the internal notes with their reasons.
Which other exams does this bank help with? +
Number problems are common to all Pakistan one-paper exams, so this bank helps FPSC, PPSC, NTS, BPSC (Balochistan), KPSC, SPSC, AJKPSC, PMS GK and CSS MPT aspirants alike.