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⁞ Problems On Numbers

Aptitude ➤ Problems On Numbers ➤ 1

In this section, questions involving a set of numbers are put in the form of a puzzle. You have to analyze the given conditions, assume the unknown numbers and form equations accordingly, which on solving yield the unknown numbers.

Question 11
Q11.  In a two-digit, 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 :
 

Answer :  24


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
⇒ 22x2 + 26x - 140 = 0
⇒ 11x2 + 13x - 70 = 0
⇒ (x - 2)(11x + 35) = 0
⇒ x = 2.

Hence, required number = 11x + 2 = 24.
⚔ DISCUSS

Question 12
Q12.  Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number is ?
 

Answer :  72


Let the second number is x, then first is 2x, and third is (1/3)(2x) or 2x/3.
⇒ 2x + x + 2x/3 = 264
⇒ 11x/3 = 264
⇒ x = 72
⚔ DISCUSS

Question 13
Q13.  What is the sum of two consecutive even numbers, the difference of whose squares is 84 ?
 

Answer :  42


Let the numbers be x and x + 2.
Then, (x + 2)2 - x2 = 84
⇒ 4x + 4 = 84
⇒ 4x = 80
⇒ x = 20.

∴ The required sum = x + (x + 2) = 2x + 2 = 42.
⚔ DISCUSS

Question 14
Q14.  The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is :
 

Answer :  23


Let the numbers be x and y.
Then, xy = 120 and x2 + y2 = 289.
⇒ (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529
⇒ x + y = √529 = 23.
⚔ DISCUSS

Question 15
Q15.  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 :
 

Answer :  400


Let the numbers be x and y.

Then, xy = 9375 and x/y = 15.


xy

= 9375/15

(x/y)

⇒ y2 = 625.
⇒ y = 25.
⇒ x = 15y = (15 x 25) = 375.

∴ Sum of the numbers = x + y = 375 + 25 = 400.
⚔ DISCUSS

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