The digits of a two-digit number are in the ratio 1 : 2 (tens : units). Reversing the digits increases the number by 36. What is the number?
Units digit = 2 × tens digit
9(b − a) = 36 → b − a = 4
2a − a = 4 → a = 4, b = 8
Number = 48
Answer: 48
Problems on Numbers · Exercise 4 of 6
65 mixed-level problems on numbers in the style of campus placement tests (TCS, Infosys, Wipro, Accenture, Cognizant, Capgemini), SSC CGL/CHSL/MTS, RRB NTPC and Group D, IBPS/SBI, UPSC CSAT and state exams.
The digits of a two-digit number are in the ratio 1 : 2 (tens : units). Reversing the digits increases the number by 36. What is the number?
Units digit = 2 × tens digit
9(b − a) = 36 → b − a = 4
2a − a = 4 → a = 4, b = 8
Number = 48
Answer: 48
A number divided by 5 gives the same result as when 20 is subtracted from it. What is the number?
x/5 = x − 20
x = 5x − 100
4x = 100 → x = 25
Answer: 25
The sum of two numbers is 22, and five times one number equals six times the other. What is the smaller number?
5a = 6b → a : b = 6 : 5
Smaller = 22 × 5/11 = 10
Answer: 10
Four times the smaller of two numbers equals three times the larger, and the larger exceeds the smaller by 5. What is the product of the numbers?
4s = 3l and l = s + 5
4s = 3s + 15 → s = 15
l = 20
Product = 300
Answer: 300
Four consecutive even numbers add up to 268. What is the smallest of them?
n + (n + 2) + (n + 4) + (n + 6) = 268
4n + 12 = 268 → n = 64
Answer: 64
A number multiplied by 7 gives 91. What is the square of the number?
7x = 91 → x = 13
x² = 169
Answer: 169
A father divides ₹ 1,200 among his three sons so that the eldest gets ₹ 100 more than the second, and the second ₹ 100 more than the youngest. How much does the eldest get?
Youngest = x; second = x + 100; eldest = x + 200
3x + 300 = 1,200 → x = 300
Eldest = 500
Answer: ₹ 500
A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, its digits are reversed. What is the number?
10a + b = 4(a + b) + 3 → 6a − 3b = 3 → b = 2a − 1
Adding 18 reverses: b − a = 2
2a − 1 − a = 2 → a = 3, b = 5
Number = 35
Answer: 35
The squares of two consecutive even numbers add up to 340. What is the sum of the numbers?
n² + (n + 2)² = 340
2n² + 4n − 336 = 0 → n² + 2n − 168 = 0
(n + 14)(n − 12) = 0 → n = 12
Numbers 12 and 14 → sum 26
Answer: 26
When 8 is added to a number, the result is three-halves of the number. What is the number?
x + 8 = 3x/2
8 = x/2
x = 16
Answer: 16
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