Problems on numbers chapter 2
Q1–10 of 60If a number is added to two-fifths of itself, the value so obtained is 455. What is the number?
Let the number be $x$.
$x + \frac{2}{5}x = 455 \implies \frac{7}{5}x = 455 \implies x = \frac{455 \times 5}{7} = 325$.
Answer: (a) 325
If a number is multiplied by two-thirds of itself, the value so obtained is 864. What is the number?
Let the number be $x$.
$x \times \left(\frac{2}{3}x\right) = 864 \implies \frac{2}{3}x^2 = 864 \implies x^2 = 1296 \implies x = 36$.
Answer: (b) 36
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?
Let the number be $x$.
$\frac{x - 4}{6} = 8 \implies x - 4 = 48 \implies x = 52$.
Now calculate: $\frac{52 - 2}{5} = \frac{50}{5} = 10$.
Answer: (b) 10
A number when multiplied by 13 is increased by 180. The number is.
Let the number be $x$.
$13x = x + 180 \implies 12x = 180 \implies x = 15$.
Answer: (c) 15
The sum of twice a number and three times of 42 is 238. What is the sum of thrice the number and two times of 42?
Let the number be $x$.
$2x + 3(42) = 238 \implies 2x + 126 = 238 \implies 2x = 112 \implies x = 56$.
Required sum: $3(56) + 2(42) = 168 + 84 = 252$.
Answer: (c) 252
If one-third of one-fourth of a number is 15, then three-tenths of that number is
Let the number be $x$.
$\frac{1}{3} \times \frac{1}{4} \times x = 15 \implies \frac{x}{12} = 15 \implies x = 180$.
Required value: $\frac{3}{10} \times 180 = 54$.
Answer: (d) 54
The difference between 3/5th of 2/3rd of a number and 2/5th of 1/4th of the same number is 288. What is the number?
Let the number be $x$.
$\left(\frac{3}{5} \times \frac{2}{3} \times x\right) - \left(\frac{2}{5} \times \frac{1}{4} \times x\right) = 288 \implies \frac{2}{5}x - \frac{1}{10}x = 288 \implies \frac{3}{10}x = 288 \implies x = 960$.
Answer: (d) 960
A number is doubled and 9 is added. If the resultant is trebled; it becomes 75. What is that number?
Let the number be $x$.
$3(2x + 9) = 75 \implies 2x + 9 = 25 \implies 2x = 16 \implies x = 8$.
Answer: (c) 8
Three-fourth of a number is 60 more than its one-third. The number is
Let the number be $x$.
$\frac{3}{4}x - \frac{1}{3}x = 60 \implies \frac{5}{12}x = 60 \implies x = 144$.
Answer: (c) 144
A number whose fifth part increased by 4 is equal to its fourth part diminished by 10, is
Let the number be $x$.
$\frac{x}{5} + 4 = \frac{x}{4} - 10 \implies \frac{x}{4} - \frac{x}{5} = 14 \implies \frac{x}{20} = 14 \implies x = 280$.
Answer: (d) 280