Average - Study Mode

[#426] A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What was the difference of the two digits a and b?
Correct Answer

(C) 2

Explanation

Solution: Let the original number be (10a + b) After interchanging the digits, the new number becomes (10b + a) The question states that the average of 10 numbers has become 1.8 less than the original average. Therefore, the sum of the original 10 numbers will be (10 × 1.8 = 18 more than the sum of the 10 numbers with the digits interchanged. 10a + b = 10b + a + 18 9a - 9b = 18 a - b = 2

[#427] The average of first five multiples of 3 is:
Correct Answer

(A) 9

Explanation

Solution: First five multiples of three are: 3, 6, 9, 12, 15. $$eqalign{
& { ext{Average}} = frac{{ {3 + 6 + 9 + 12 + 15} }}{5} cr
& ,,,,,,,,,,,,,,,,,,,,,,,, = frac{{45}}{5} cr
& ,,,,,,,,,,,,,,,,,,,,,,,, = 9 cr} $$ Alternatively ,
Average = $$frac{{ {3 + 15} }}{2} = 9$$

[#428] There are two sections A and B of a class, consisting of 36 and 44 students' respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class.
Correct Answer

(D) 37.25 kg

Explanation

Solution: The total weight of (36 + 44) Students of A and B, = (36 × 40 + 44 × 35) kg = 2980 kg. Therefore average weight of the whole class = $$frac{{2980}}{{80}}$$ kg Therefore average weight = 37.25 kg

[#429] Distance between two stations A and B is 778km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km per hour. Find the average speed of train during the whole journey.
Correct Answer

(D) 67.2 km/hr

Explanation

Solution: The required average speed given by the formula, $$eqalign{
& { ext{Average speed}} cr
& = {frac{{2xy}}{{ {x + y} }}} ,,{ ext{km/hr}} cr
& { ext{Where}}, cr
& x = 84{kern 1pt} ,{ ext{kmph}} cr
& y = 56,{kern 1pt} { ext{kmph}} cr
& { ext{Average speed}} cr
& = {frac{{ {2 imes 84 imes 56} }}{{ {84 + 56} }}} cr
& = 67.2,{kern 1pt} { ext{kmph}} cr} $$

[#430] A batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 3. Find his average after 17 th inning.
Correct Answer

(B) 39

Explanation

Solution: Let the average after 17 th innings = x Then average after 16 th innings = (x - 3) Therefore 16 × (x - 3) + 87 = 17x Therefore x = 39