Average - Study Mode

[#221] The speed of the train going from Nagpur to Allahabad is 100 km/h while when coming back from Allahabad to Nagpur, its speed is 150 km/h. find the average speed during whole journey.
Correct Answer

(D) 120 km/hr

Explanation

Solution: $$eqalign{
& { ext{Average speed}}, cr
& = frac{{ {2 imes x imes y} }}{{ {x + y} }} cr
& = frac{{ {2 imes 100 imes 150} }}{{ {100 + 150} }} cr
& = frac{{ {200 imes 150} }}{{250}} cr
& = 120,{ ext{km/hr}} cr} $$

[#222] Find the average of first 97 natural numbers.
Correct Answer

(D) 49

Explanation

Solution: 1 st Method: Average of 1 st n natural number is given by $$ = frac{{ {frac{{ {{ ext{n}} imes left( {{ ext{n}} + 1}
ight)} }}{2}} }}{{ ext{n}}}$$ Average of 1 st 97 natural number is given by $$eqalign{
& {frac{{ {frac{{ {97 imes left( {97 + 1}
ight)} }}{2}} }}{{97}}} cr
& = 49 cr} $$ 2 st Method: These numbers are in AP series so average. $$eqalign{
& = frac{{ {{ ext{sum of corresponding term}}} }}{2} cr
& = frac{{ {1 + 97} }}{2} = 49 cr
& { ext{or, }}frac{{ {2 + 96} }}{2} = 49 cr
& { ext{or, }}frac{{ {3 + 95} }}{2} = 49 cr
& { ext{And so on}}{ ext{.}} cr} $$

[#223] The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest boy is
Correct Answer

(D) 9 years

Explanation

Solution: Sum of ages of three boys = 45 years Now, (3x + 5x + 7x) = 45 ⇒ 15x = 45 ⇒ x = 3 So, age of youngest boy = 3x = 3 × 3 = 9 years

[#224] In a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man. What is weight of new comer?
Correct Answer

(C) 68 kg

Explanation

Solution: Member in group × age increased = difference of replacement Or, 8 × 1 = new comer - man going out Or, new comer = 8 + 60 Or, new comer = 68 kg.

[#225] The average of 25 results is 18. The average of first 12 of those is 14 and the average of last 12 is 17. What is the 13 th result?
Correct Answer

(D) 78

Explanation

Solution: Sum of 1 st 12 results = 12 × 14 Sum of last 12 results = 12 × 17 13 th result = x (let) Now, 12 × 14 + 12 × 17 + x = 25 × 18 Or, x = 78