Average - Study Mode

[#316] The average of thirteen numbers is 80. The average of the first five numbers is 74.5 and that of the next five numbers is 82.5. The 11 th number is 6 more than the 12 th number is 6 less than the 13 th number. What is the average of the 11 th and the 13 th numbers?
Correct Answer

(A) 87

Explanation

Solution: Average of 13 numbers = 80 ⇒ Sum of 13 numbers = 80 × 13 = 1040 Average of the first 5 numbers = 74.5 ⇒ Sum of the first 5 numbers = 74.5 × 5 = 372.5 Average of next 5 numbers (6 th to 10 th ) = 82.5 ⇒ Sum of the next 5 numbers (6 th to 10 th ) = 82.5 × 5 = 412.5 ⇒ Sum of the last 3 numbers = 1040 - 372.5 - 412.5 = 255 Let the 12 th number be x 11 th number = x + 6 and 13 th number = x + 6 According to the question, ⇒ x + 6 + x + x + 6 = 255 ⇒ x = 81 ⇒ 11 th number = x + 6 = 81 + 6 = 87 ⇒ 13 th number = x + 6 = 81 + 6 = 87 ∴ Average of 11 th and 13 th number = $$frac{{87 + 87}}{2}$$ xa0= 87

[#317] Average of all even numbers between 222 and 250 is . . . . . . . .
Correct Answer

(C) 236

Explanation

Solution: $$eqalign{
& { ext{Numbers are }}224,,226,,.....,248 cr
& {S_n} = frac{{13}}{2}left[ {224 + 248}
ight] cr
& = frac{{13}}{2} imes 472 cr
& { ext{Average}} = frac{{13 imes 472}}{{2 imes 13}} = 236 cr
& cr
& {x08f{Alternate:}} cr
& { ext{Average of all even number between }}222{ ext{ and }}250 cr
& Rightarrow a = 224 cr
& l = 248 cr
& { ext{Average}} = frac{{a + l}}{2} cr
& = frac{{224 + 248}}{2} cr
& = 236 cr} $$

[#318] Average of first five odd multiples of 3 is
Correct Answer

(C) 15

Explanation

Solution: According to the question, First five odd multiples of 3 is = 3, 9, 15, 21, 27 $$eqalign{
& herefore { ext{Average}} = frac{{3 + 9 + 15 + 21 + 27}}{5} cr
& = frac{{75}}{5} cr
& = 15 cr} $$

[#319] The average of 33 numbers is 74. The average of the first 17 numbers is 72.8 and that of the last 17 numbers is 77.2. If the 17 th number is
excluded, then what will be the average of the remaining numbers (correct to one decimal place)?
Correct Answer

(A) 72.9

Explanation

Solution: Average of 33 members = 74 Sum of numbers = 33 × 74 = 2442 Sum of the first 17 numbers = 1237.6 Sum of the last 17 numbers = 17 × 77.2 = 1312.4 17 th number = 1237.6 + 1312.4 - 2442 = 108 Average of 32 numbers $$ = frac{{2442 - 108}}{{32}} = 72.9$$

[#320] The arithmetic mean (average) of the first 10 whole number is
Correct Answer

(D) 4.5

Explanation

Solution: According to the question, First 10 whole numbers are = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ∴ Average of 10 whole numbers $$eqalign{
& = frac{{0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9}}{{10}} cr
& = frac{{45}}{{10}} cr
& = 4.5 cr} $$