Question

The average price of three books is 16. The prices of two of the books is given by the following pairs. Which is the correct pair?
(A) 23 and 27
(B) 20 and 23
(C) 25 and 26
(D) 24 and 25​

Answer 1

Given :-

• The average price of three books is ₹16

Aim :-

• To find the prices of book 1 and book 2 respectively from the given options
• ₹23 and ₹27
• ₹20 and ₹23
• ₹25 and ₹26
• ₹24 and ₹25

Answer :-

Concept applied :-

Average is the number expressing the central/typical or the overall value of any number of quantities.

The average is calculated by using the formula :-

$\boxed {\longrightarrow \sf\dfrac{sum\: of \: all\: observations}{total\:number\:of\:observations}}$

Solution :-

Let the three book's prices be ₹x, ₹y and ₹z respectively.

Accordingly,

$\implies \sf \dfrac{x+y+z}{3} = 16$

Transposing 3 to the RHS (Right hand side of the equation),

$\implies \sf x+y+z = 16 \times 3$

$\implies \sf x+y+z = 48$

The total sum of the three book's prices is ₹48. Hence, the correct pair from the given sets must be :-

→ x+y < 48

(Lesser than 48)

Option A :-

The prices given are ₹23 and ₹27

By adding both of them,

⇒ 50

Clearly,

→ 50 > 48.

∴ It cannot be option (a).

Option B :-

Given prices are ₹20 and ₹23.

Adding the numbers,

⇒ 43

→ 43< 48.

∴ Option (b) is correct.

Option C :-

Prices are ₹25 and ₹26

Adding them,

⇒ ₹51

→ 51 > 48

∴Option (c) is incorrect

Option D :-

The prices given are ₹24 and ₹25.

Adding them,

⇒ ₹49

Clearly,

→ 49 > 48

∴ This option (d) is incorrect.

By the above observations, we can conclude that Option (B) is correct.

Answer 2

step_by_step explanation