Question 1

Three numbers are in the ratio 4 : 5 : 6 and their average is 25. The largest number is :

Accepted Answer

Let the numbers be 4x, 5x and 6x, Then, (4x + 5x + 6x ) / 3 = 25 => 5x = 25 => x = 5. Largest number 6x = 30.

Question 2

The difference between the two numbers is 1365. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is?

Accepted Answer

Let the numbers be x and 1365+x Then 1365+x = 6x+15 => x = 270

Question 3

The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is :

Accepted Answer

Let the numbers be x and y. Then, xy = 9375 and x/y = 15. x y x y = 9375 / 15 => y 2 = 625 => y = 25 => x = 15y = 15 x 25 = 375. Sum of the numbers = 375 + 25 = 400.

Question 4

In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is :

Accepted Answer

Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2 Sum of digits = x + (x + 2) = 2x + 2. (11x + 2) (2x + 2) = 144 => 22x^2+26x-140=0 => (x - 2)(11x + 35) = 0 => x = 2 Hence, Required Number = 11x + 2 = 24

Question 5

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 ?

Accepted Answer

Let the numerator be x Then, denominator = x + 3. Now. (x + 4)/(x + 3) +4 = 4/5 <=> 5 (x + 4) = 4(x + 7) => x = 8. The fraction is 8/11.

Question 6

What approximate value will come in place of the question mark(?) in the below question? (47% of 1442 - 36% of 1412) + 63 = ?

Accepted Answer

3

Question 7

There are two numbers such that the sum of twice the first and thrice the second is 39, while the sum of thrice the first, and twice the second is 36. The larger of the two is :

Accepted Answer

Let the numbers be x and y. Then, 2x + 3y = 39...(i)and 3x + 2y = 30 ...(ii) On solving (i) and (ii), we get : x = 6 and y = 9. larger number = 9

Question 8

12 students of class IX took part in GK quiz. If the number of boys is 4 more than the number of girls. Find the number of boys and girls took part in the quiz ?

Accepted Answer

Let the number of girls = x => x + x + 4 = 12 => 2x = 8 => x = 4 => Number of girls = 4 => Number of boys = 4 + 4 = 8

Question 9

The product of three consecutive even numbers when divided by 8 is 720. The product of their square roots is :

Accepted Answer

Let the numbers be x, x + 2 and X + 4. Then, x(x + 2)(x +4) / 8 = 720 => x(x + 2)(x +4) = 5760. √x * √(x + 2) * √(x +4) = √x(x +2)(x + 4 ) = √5760 = 24√10.

Question 10

In the following question a number series is given which has only one wrong number. You have to find out the wrong number? 7.5 47.5 87.5 157.5 247.5 357.5 487.5

Accepted Answer

47.5

Question 11

A fraction becomes 2/3 when 1 is added to both, its numerator and denominator. And, it becomes 1/2 when 1 is subtracted from both the numerator and denominator. What is the fraction?

Accepted Answer

Let the required fraction be x/y. Then, x+1 / y+1 = 2 / 3 => 3x  2y = - 1 (i) and x  1 / y  1 = 1 / 2 2x  y = 1 (ii) Solving (i) and (ii), x = 3 , y = 5 therefore, Required fraction= 3/5

Question 12

There are four prime numbers written in ascending order of magnitude. The product of the first three is 385 and of the last three is 1001. Find the fourth number ?

Accepted Answer

(385/1001) = 5/13 First Number is 5 => Fourth number is 13

Question 13

54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :

Accepted Answer

Let the two parts be (54 - x) and x. Then, 10 (54 - x) + 22x = 780 => 12x = 240 => x = 20. Bigger part = (54 - x) = 34.

Question 14

Find the number which when multiplied by 15 is increased by 196.

Accepted Answer

Let the number be x. Then, 15x - x = 196 <=> 14x = 196 => x = 14..

Question 15

The sum of the squares of two numbers is 3341 and the diference of their squares is 891. The numbers are :

Accepted Answer

Let the numbers be x and y. Then, x^2+y^2=3341......(1) x^2-y^2=891......(2) Adding (i) and (ii), we get : 2x^2=4232 or x^2= 2116 or x =46 Subtracting (ii) from (i), we get : 2y^2= 2450 or y^2 = 1225 or y = 35 So, the numbers are 35 and 46

Question 16

A number is 2 more than thrice the second number and 4 times the smaller number is 5 more than the greater number. What is greater number ?

Accepted Answer

Let the greater and smaller number be p and q respectively. 4q = p + 5 ------ (I) p = 3q+2 ------- (II) From equation (I) and (II) q = 7 p = 23

Question 17

On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is ?

Accepted Answer

By hit and trail, we find that 47619 x 7 = 333333. 7) 333333 (47619 333333 ---------------- 0 And 476190476 x 7 = 3333333333 but smallest number is 47619.

Question 18

How many numbers up to 101 and 300 are divisible by 11 ?

Accepted Answer

(300 – 101)/11 = 199/11 = 18 1/11 18 Numbers.

Question 19

Sum of two numbers is 44. One number is 3 times as large as the other. What are the numbers?

Accepted Answer

Let the smaller number be 'm' Then, from the given data, the larger number is '3m' Given that m + 3m = 44 => 4m = 44 m = 44/4 = 11 => m = 11 => 3m = 3 x 11 = 33 Hence, the two numbers are 11 and 33.

Question 20

If the product of 6 integers is negative, at most how many of the integers can be negative?

Accepted Answer

Multiplying two negatives (or any even multiple) results in a positive. But multiplying three negatives (or any odd multiple) gives a negative. If the result of multiplying 6 negatives is odd, the largest number of negative integers will be the largest odd number (i.e.5)

Problems on Numbers Questions