If p, q, r, be three positive numbers such that p > q > r when the sma

1.	If p, q, r, be three positive numbers such that p > q > r when the smallest number is added to the difference of the rest two numbers, then the average of the resultant number and the original numbers except to the smallest number is 21 more than the average of all the three original numbers. What is the value of (p - q)?1). 442). 1893). 214). 63
Answer» We KNOW that, FORMULA for average: ⇒ $(\left\{ {{A_E} = \FRAC{{{S_E}}}{{{n_E}}}\;or\;{S_E} = {A_E} \times {n_E}} \right\})$ where, S_E = Sum of entities, n_E = Number of entities, A_E= Average of entities. Now, according to the question: $(\frac{{\left[ {r + \left( {p - Q} \right)} \right] + \;p + q}}{3} = 21 + \frac{{p + q + r}}{3})$ $(\Rightarrow \frac{{2p + r}}{3} - \;21 = \frac{{p + q + r}}{3})$ $(\Rightarrow \frac{{p - q}}{3} = 21)$ ⇒ p – q = 63 ∴ T$he required value of (p - q) is 63

If p, q, r, be three positive numbers such that p > q > r when the smallest number is added to the difference of the rest two numbers, then the average of the resultant number and the original numbers except to the smallest number is 21 more than the average of all the three original numbers. What is the value of (p - q)?1). 442). 1893). 214). 63

Answer»

We KNOW that, FORMULA for average:

⇒ $(\left\{ {{A_E} = \FRAC{{{S_E}}}{{{n_E}}}\;or\;{S_E} = {A_E} \times {n_E}} \right\})$

where,

S_E = Sum of entities,

n_E = Number of entities,

A_E= Average of entities.

Now, according to the question:

$(\frac{{\left[ {r + \left( {p - Q} \right)} \right] + \;p + q}}{3} = 21 + \frac{{p + q + r}}{3})$

$(\Rightarrow \frac{{2p + r}}{3} - \;21 = \frac{{p + q + r}}{3})$

$(\Rightarrow \frac{{p - q}}{3} = 21)$

⇒ p – q = 63

∴ T$he required value of (p - q) is 63