A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) Rs. 4991
(B) Rs. 5991
(C) Rs. 6001
(D) Rs. 6991
Solution:
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009 ∴ Required sale = Rs. [(6500 × 6) - 34009] = Rs. (39000 - 34009) = Rs. 4991
442.
One-fourth of certain journey is covered at the rate of 25 km/h, one-third at the rate of 30 km/h and the rest at 50 km/h. Find the average speed for the whole journey.
(A) $$\frac{{600}}{{53}}$$ km/h
(B) $$\frac{{1200}}{{53}}$$ km/h
(C) $$\frac{{1800}}{{53}}$$ km/h
(D) $$\frac{{1600}}{{53}}$$ km/h
Solution:
Let distance be 120 km Hence 30 km is covered by @25 kmph and 40 km covered by @30 kmph and rest 50 km has been covered @50 kmph Now, $$\eqalign{ & {\text{average}} = {\frac{{120}}{{{\text{total}}\,{\text{time}}\,{\text{taken}}}}} \cr & = \frac{{120}}{{\frac{{30}}{{25}} + \frac{{40}}{{30}} + \frac{{50}}{{50}}}} \cr & = \frac{{3600}}{{106}} \cr & = \frac{{1800}}{{53}}\,{\text{km/h}} \cr} $$
443.
Mean of 10 numbers is 30. Later on it was observed that numbers 15, 23 are wrongly taken as 51, 32. The correct mean is :
(A) 25.5
(B) 32
(C) 30
(D) 34.5
Solution:
According to the question, Mean of 10 numbers is = 30 ∴ Sum of 10 numbers is = 300 It was observed that numbers 15, 23 are wrongly taken as 51, 32 Difference = (51 + 32) - (15 + 23) = 83 - 38 = 45 (more) ∴ Actual sum of 10 numbers = 300 - 45 = 255 ∴ Actual average of 10 numbers = $$\frac{255}{10}$$ = 25.5
444.
A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) Rs. 4991
(B) Rs. 5991
(C) Rs. 6001
(D) Rs. 6991
Solution:
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009 Therefore Required sale = Rs. [(6500 × 6) - 34009] = Rs. (39000 - 34009) = Rs. 4991
445.
The average of ten numbers is 7. If each number is multiplied by 12, then the average of the new set of numbers is :
(A) 7
(B) 19
(C) 82
(D) 84
Solution:
Average of 10 numbers = 7 Sum of these 10 numbers = (10 × 7) = 70 $$\eqalign{ & \therefore {x_1} + {x_2} + ..... + {x_{10}} = 70 \cr & \Rightarrow 12{x_1} + 12{x_2} + ..... + 12{x_{10}} = 840 \cr & \Rightarrow \frac{{12{x_1} + 12{x_2} + ..... + 12{x_{10}}}}{{10}} = 84 \cr} $$ ⇒ Average of new numbers is 84
446.
The average monthly income of a family of four earning members was Rs. 15130. One of the daughters in the family got married and left home, so the average monthly income of the family came down to Rs. 14660. What is the monthly income of the married daughter?
(A) Rs. 12000
(B) Rs. 15350
(C) Rs. 16540
(D) Cannot be determined
Solution:
Monthly income of the married daughter = Rs. (15130 × 4 - 14660 × 3) = Rs. (60520 - 43980) = Rs. 16540
447.
The average of 8 numbers is 20. The average of first two numbers is $$15\frac{1}{2}$$ and that of the next three is $$21\frac{1}{3}$$. If the sixth number be less than the seventh and eighth numbers by 4 and 7 respectively, then the eight number is-
(A) 18
(B) 22
(C) 25
(D) 27
Solution:
Let the eight number be x Then, sixth number = (x - 7) Seventh number = (x - 7) + 4 = (x - 3) So, $$ \Leftrightarrow \left( {2 \times 15\frac{1}{2}} \right) + \left( {3 \times 21\frac{1}{2}} \right)$$ $$ + \left( {x - 7} \right)$$ $$ + \left( {x - 3} \right)$$ $$ + \,x = 8 \times 20$$ $$\eqalign{ & \Leftrightarrow 31 + 64 + \left( {3x - 10} \right) = 160 \cr & \Leftrightarrow 3x = 75 \cr & \Leftrightarrow x = 25 \cr} $$
448.
The average of runs of a cricket player of 10 innings was 32. How many runes must be made in his next innings so as to increase his average of runs by 4?
(A) 72
(B) 74
(C) 70
(D) 76
Solution:
Average after 11 innings = 36 Required number of runs, = ( 36 × 11) - (32 × 10) = 396 - 320 = 76
449.
Visitor to a show were charged Rs. 15 each on the first day, Rs. 7.50 each on the second day and Rs. 2.50 each on the third day. The attendance on the three days was in the ratio 2 : 5 : 13. The average charge per person for the whole show was-
(A) Rs. 5
(B) Rs. 6.33
(C) Rs. 7.50
(D) Rs. 9
Solution:
Let the attendance on the three days be 2x, 5x and 13x respectively. Then, total charges = Rs. (15 × 2x + 7.50 × 5x + 2.50 × 13x) = Rs. (30x + 37.5x + 32.5x) = Rs. 100x ∴ Average change per person = Rs. $$\left( {\frac{{100x}}{{2x + 5x + 13x}}} \right)$$ = Rs. 5
450.
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.