Question 1

A natural number when increased by 12 equals 160 times its reciprocal. Find the number?

Accepted Answer

Let the required number be 'p'. From the given data, p + 12 = 160 x 1/p => p + 12 = 160/p => p(p + 12) = 160 => P^2 + 12p - 160 = 0 => p^2 + 20p - 8p - 160 = 0 => P(p + 20) - 8(p + 20) = 0 => (p + 20)(p - 8) = 0 => p = -20 or p = 8 As, given the number is a natural number, so it can't be negative. Hence, the required number p = 8.

Question 2

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 ?

Accepted Answer

Let the number be x. Then, 2/3x-50 = 1/4x +50 => 5/12x = 90 x = (90 x 12) / 5 = 216

Question 3

The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers ?

Accepted Answer

Let the ten's digit be x and unit's digit be y. Then, (10x + y) - (10y + x) = 63 => 9 (x - y) = 63 => x - y = 7. Thus, none of the numbers can be deermined..

Question 4

If 78K928L is divisible by 6, then which of the following can Q and R take ?

Accepted Answer

As per divisibility rule a number is divisible by 6 means it should be divisible by 2 and 3 case 1 : the divisibility rule for 2 is the number should be end with even number in this case R =2 & R=4 case 2 : The divisibility rule for 3 is the sum of numbers should be divisible by 3 so if we take option (2) Q=1 & R=4 the sum is 39 if we take option (3) Q=1 & R=2 the sum is 37 So Option (2) is correct 39 is divided by 3

Question 5

The sum of one-half, one-third and one-fourth of a number exceeds the number by 22. The number is

Accepted Answer

Let the number be 'x'. Then, from given data x/2 + x/3 + x/4 = x+22 13x/12 = x+22 x = 264

Question 6

Find the least number with which 16200 should be multiplied, to make it a perfect cube ?

Accepted Answer

16200 = 2 3 × 3 4 × 5 2 A perfect cube has a property of having the indices of all its prime factors divisible by 3. Required number = 3 2 × 5 = 9x5 = 45.

Question 7

96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part ?

Accepted Answer

Let x and y be the two parts of 96. x/7 = y/9 => x:y = 7:9 => The smallest part is = 7/16 x 96 = 42.

Question 8

On dividing a number by 96, we get 271 as quotient and 0 as remainder. On dividing the same number by 95, what will be the remainder ?

Accepted Answer

Number = 271 x 96 + 0 = 26016 => 95) 26016 (273 25935 -------- 81 Required number = 81.

Question 9

The ratio of two positive numbers is 3 : 5 and the average of the number is 48. What is the product of numbers?

Accepted Answer

Let the number be 3p and 5p ATQ, 8p = 2 x 48 p = 96/8 p = 12 The numbers are 36 and 60. Hence, the product of the numbers = 36 x 60 = 2160.

Question 10

The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number?

Accepted Answer

Let the larger number be p Then, smaller number = 1/6 x p = p/6 Given difference between two numbers = 25 p - p/6 = 25 5p/6 = 25 5p = 150 p = 30 Then, p/6 = 30/6 = 5 Hence, larger number = 30 and smaller number = 5 which makes the difference = 25.

Question 11

A text book of mathematics cost 2 Rs/- more than a text book of literature. If 5 literature books cost 38 Rs/- more than 3 mathematics books, what is the cost of each literature book?

Accepted Answer

Let each literature text book cost be Rs. X Then, cost of mathematics text book = Rs. (X + 2) ATQ, 5X = 38 + 3(X + 2) 5X = 38 + 3X + 6 2X = 44 X = 22. Therefore, cost of each literature text book = Rs. X = Rs. 22. And that of masthematics = X + 2 = Rs. 24.

Question 12

The largest 4 digit number exactly divisible by 88 is

Accepted Answer

To find the largest 4 digit number exactly divisible by 88, We should divide the largest possible 4 digit number by 88, and if we get any remainder than subtract it from that largest number. The largest possible 4 digit number is 9999 Now, 88) 9999 (113 88 _______ 119 88 _______ 319 264 _______ 55 _______ Therefore, the largest 4 digit number exactly divisible by 88 is given by 9999 - 55 = 9944.

Question 13

A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is :

Accepted Answer

Let the middle digit be x. Then, 2x = 10 or x = 5. So, the number is either 253 or 352 Since the number increases on reversing the digits, so the hundred's digit is smaller than the unit's digit. Hence, required number = 253.

Question 14

If two painters can complete two rooms in two hours, how many painters would it take to do 18 rooms in 6 hours?

Accepted Answer

Two painters can complete two rooms in two hours.So 18 rooms can be painted in 6 hrs by 6 painters

Question 15

A person walking 6/7 of his usual rate is 30 minutes late. What is his usual time ?

Accepted Answer

Let t be the usual time. If the usual rate is 1 unit, then the unusual rate is 6/7. Balance by the distance, 1 x t = (6/7)(t + 30) 7t = 6(t + 30) we get t as, t = 180 minutes = 3 hrs.

Question 16

Find the number which multiplied by 15 is increased by 56 ?

Accepted Answer

Let the number be x. Then, 15x - x = 56 x = 4

Question 17

What is the common ratio of the following geometric sequence? 4, 2, 1, 0.5, 0.25, 0.125,...

Accepted Answer

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. Herein the given sequence, 4, 2, 1, 0.5, 0.25, 0.125,... Common Ratio r = 2/4 = 1/2 = 0.5/1 = 0.25/0.5 = 0.125/0.25 == 0.5.

Question 18

A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number ?

Accepted Answer

Let the number be v. Then, 3 (2x + 9) = 75. 2x + 9 = 25 => 2x = 16 => x = 8

Question 19

If 1 is added to the denominator of a traction, the fraction becomes 1/2. If 1 is added to the numerator of the fraction, the fraction becomes 1. The fraction is :

Accepted Answer

Let the fraction be x/y. Then, x /(y+1) = 1/2 => 2x - y = 1 ..........(i)and (x + 1) / y = 1 => x - y = 1 .......(ii) Solving (i) and (ii), we get : x = 2, y = 3. Hence, the required fraction is 2/3..

Question 20

The sum of the digits of a two-digit number is 9 less than the number. Which of the following digits is at unit's place of the number ?

Accepted Answer

Let the ten's digit be x and unit's digit be y. Then, (10x + y) - (x + y) = 9 or x = 1. From this data we cannot find y, the unit's digit. So the data is inadequate..

Problems on Numbers Questions