Three numbers A, B and C are in the ratio 1 : 2 : 3. Their average is

1.	Three numbers A, B and C are in the ratio 1 : 2 : 3. Their average is 600. If A is increased by 10% and B is decreased by 20%, then by how much will C be increased to get the average increased by 5% ?
Answer» Let A = x, B = 2x and C = 3x Given, \(\frac{x+2x+3x}{3}\) = 600 ⇒ 6x = 1800 ⇒ x = 300 ∴ The numbers are A = 300, B = 600, C = 900 New average = 105% of 600 = \(\frac{105}{100}\times600\) = 630 New value of A = \(\frac{110}{100}\times300\) = 330 New value of B = \(\frac{80}{100}\times600\) = 480 Let new value of C = y Then, \(\frac{330+480+y}{3}\) = 630 ⇒ 810 + y = 1890 ⇒ y = 1080 ∴ Increase in C = 1080 – 900 = 180.

Three numbers A, B and C are in the ratio 1 : 2 : 3. Their average is 600. If A is increased by 10% and B is decreased by 20%, then by how much will C be increased to get the average increased by 5% ?

Answer»

Let A = x, B = 2x and C = 3x

Given, \(\frac{x+2x+3x}{3}\) = 600 ⇒ 6x = 1800 ⇒ x = 300

∴ The numbers are A = 300, B = 600, C = 900

New average = 105% of 600 = \(\frac{105}{100}\times600\) = 630

New value of A = \(\frac{110}{100}\times300\) = 330

New value of B = \(\frac{80}{100}\times600\) = 480

Let new value of C = y

Then, \(\frac{330+480+y}{3}\) = 630 ⇒ 810 + y = 1890

⇒ y = 1080 ∴ Increase in C = 1080 – 900 = 180.