The sum of two numbers is 4000. 10% of one number is 6\(\frac{2}{3}\)%

1.	The sum of two numbers is 4000. 10% of one number is 6\(\frac{2}{3}\)% of the other. The difference of the number is (a) 600 (b) 800 (c) 1025 (d) 1175
Answer» (b) 800 Let one number = x Then, the other number = 4000 – x Given, 10% of x = 6\(\frac{2}{3}\)% of (4000-x) \(\Rightarrow\) \(\frac{10}{100}\) x x = \(\frac{20}{3}\) x \(\frac{1}{100}\) x (4000-x) \(\Rightarrow\) 10x = \(\frac{20}{3}\) x 4000 - \(\frac{20X}{3}\) \(\Rightarrow\) 10x + \(\frac{20X}{3}\) = \(\frac{20}{3}\) x 4000 \(\Rightarrow\) \(\frac{50X}{3}\) = \(\frac{20}{3}\) x 4000 \(\Rightarrow\) x = \(\frac{20\times4000}{50}\) = 1600 The two numbers are 1600 and 2400. \(\therefore\) Their difference = 2400 – 1600 = 800.

The sum of two numbers is 4000. 10% of one number is 6\(\frac{2}{3}\)% of the other. The difference of the number is (a) 600 (b) 800 (c) 1025 (d) 1175

Answer»

(b) 800

Let one number = x

Then, the other number = 4000 – x

Given, 10% of x = 6\(\frac{2}{3}\)% of (4000-x)

\(\Rightarrow\) \(\frac{10}{100}\) x x = \(\frac{20}{3}\) x \(\frac{1}{100}\) x (4000-x)

\(\Rightarrow\) 10x = \(\frac{20}{3}\) x 4000 - \(\frac{20X}{3}\)

\(\Rightarrow\) 10x + \(\frac{20X}{3}\) = \(\frac{20}{3}\) x 4000

\(\Rightarrow\) \(\frac{50X}{3}\) = \(\frac{20}{3}\) x 4000

\(\Rightarrow\) x = \(\frac{20\times4000}{50}\) = 1600

The two numbers are 1600 and 2400.

\(\therefore\) Their difference = 2400 – 1600 = 800.