Average - Study Mode

[#216] 3 years age, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is same today. The present age of the baby is :
Correct Answer

(C) 2 years

Explanation

Solution: According to the question, Average age of a family of 5 members 3 years ago = 17 years sum of ages of a family members = 5 × 17 = 85 years A baby having been born the average age of the family is same today. ∴ Sum of age of a family of 6 members = 17 × 6 = 102 years ∴ Sum of age of a family of 5 members at present = 85 + 5 × 3 = 85 + 15 = 100 years ∴ Age of child = 102 - 100 = 2 years

[#217] The average age of P, Q and R is 15 years more than R's age. If the total age of P and Q together is 39 years, then R's age is ?
Correct Answer

(A) 12 years

Explanation

Solution: $$frac{P + Q + R}{3}$$ xa0 = R + 5 P + Q + R = 3R + 15 P + Q - 2R = 15 . . . . . (i) P + Q= 39 . . . . . (ii) From equation (i) and (ii) 39 - 2R = 15 2R = 24 R = 12 years

[#218] Find the average of 1.11, 0.01, 0.101, 0.001, 0.11 = ?
Correct Answer

(A) 0.2664

Explanation

Solution: According to the question, Average = $$frac{1.11 + 0.01 + 0.101 + 0.001 + 0.11 }{5}$$ = $$frac{1.332}{5}$$ = 0.2664

[#219] Ajit has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average by 8 runs. His new average is:
Correct Answer

(C) 28

Explanation

Solution: Let Ajit's average be x for 9 innings. So, Ajit scored 9x run in 9 innings. In the 10 th inning, he scored 100 runs then average became (x+8). And he scored (x + 8) × 10 runs in 10 innings. Now, $$eqalign{
& Rightarrow 9x + 100 = 10 imes left( {x + 8}
ight) cr
& { ext{or}},,9x + 100 = 10x + 80 cr
& { ext{or}},,x = 100 - 80 cr
& { ext{or}},,x = 20 cr
& { ext{New}},{ ext{average}} = left( {x + 8}
ight) cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, = 28,{ ext{runs}} cr} $$

[#220] The average of the first five multiples of 9 is:
Correct Answer

(B) 27

Explanation

Solution: $$eqalign{
& { ext{Required}},{ ext{average}} cr
& = {frac{{{ ext{total}},{ ext{sum}},{ ext{of}},{ ext{multiple}},{ ext{of}},9}}{5}} cr
& = {frac{{9 + 18 + 27 + 36 + 45}}{5}} cr
& = 27 cr} $$ Note that, average of 9 and 45 is also 27. And average of 18 and 36 is also 27.