Directions (1-5): A soft-drink company prepares drinks of three different flavours – X, Y and Z. The production of the three flavours over a period of six years has been expressed in the bar-graph provided below. Study the graph and answer the questions based on it.
Production of three different flavours of soft-drinks X, Y, Z by a
Company over the year (in lakh bottles)
Q1. For which of the following years the percentage of rise/fall in production from the previous year is the maximum for the flavor Y?
(a) 1996
(b) 1997
(c) 1998
(d) 1999
(e) 2000
Q2. For which flavor was the average annual production maximum in the given period?
(a) X only
(b) Y only
(c) Z only
(d) X and Y
(e) X and Z
Q3. The total production of flavor Z in 1997 and 1998 is what percentage of the total production of flavor X in 1995 and 1996?
(a) 96.67%
(b) 102.25%
(c) 115.57%
(d) 120%
(e) 133.33%
Q4. What is the difference between the average production of flavor X in 1995, 1996 and 1997 and the average production of flavor Y in 1998, 1999 and 2000?
(a) 50,000 bottles
(b) 80,000 bottles
(c) 2,40,000 bottles
(d) 3,30,000 bottles
(e) 5,00,000 bottles
Q5. What was the approximate decline in the production of flavor Z in 2000 as compared to the production in 1998?
(a) 50%
(b) 42%
(c) 33%
(d) 25%
(e) 22.5%
Directions (6-10): The bar-graph given below shows the percentage distribution of the total production of a car manufacturing company into various models over two years. Study the graph carefully and answer the questions that follow.
Percentage of Six different types of Cars manufactured by a Company over two years
Q6. Total number of cars of models P, Q and T manufactured in 2000 is:
(a) 2,45,000
(b) 2,27,500
(c) 2,10,000
(d) 1,92,500
(e) 1,57,500
Q7. For which model the percentage rise/fall in production from 2000 to 2001 was minimum?
(a) Q
(b) R
(c) S
(d) T
(e) U
Q8. What was the difference in the number of Q type cars produced in 2000 and that produced in 2001?
(a) 35,500
(b) 27,000
(c) 22,500
(d) 17,500
(e) 16,000
Q9. If the percentage production of P type cars in 2001 was the same as that in 2000, then the number of P type cars produced in 2001 would have been:
(a) 1,40,000
(b) 1,32,000
(c) 1,17,000
(d) 1,05,000
(e) 97,000
Q10. If 85% of the S type cars produced in each year were sold by the Company, how many S type cars remained unsold?
(a) 7650
(b) 9350
(c) 11,850
(d) 12,250
(e) 13,350
Q11. A box contains 4 red balls, 5 green balls and 6 white balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green?
(a) 2/5
(b) 3/5
(c) 1/5
(d) 7/15
(e) None of these
Q12. In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
(a) 21/46
(b) 25/117
(c) 1/50
(d) 3/25
(e) None of these
Q13. Four persons are chosen at random from a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is:
(a) 1/9
(b) 1/5
(c) 1/12
(d) 10/21
(e) None of these
Q14. A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective, is:
(a) 4/19
(b) 7/19
(c) 12/19
(d) 21/95
(e) None of these
Q15. In a class, 30% of the students offered English, 20% offered Hindi and 10% offered both. If a student is selected at random, what is the probability that he has offered English or Hindi?
(a) 2/5
(b) 3/4
(c) 3/5
(d) 3/10
(e) None of these
Solutions
S1. Ans.(b)
Sol. The percentage rise/fall in production from the previous year for flavor Y during various years are:
S2. Ans.(b)
Sol. Average annual productions over the given period for various flavours are:
For flavour X = [1/6×(50+40+55+45+60+50)] lakh bottles = 50 lakh bottles.
For flavour Y = [1/6×(55+60+50+55+50+55)] lakh bottles
= 54.17 lakh bottles.
For flavour Z = [1/6×(45+50+60+60+45+40)] lakh bottles = 50 lakh bottles.
∴ Maximum average production is for flavor Y.
S6. Ans.(c)
Sol. We shall first determine the number of cars of each model produced by the Company during the two years:
In 2000: Total number of cars produced = 3,50,000.
P = (30 – 0)% of 3,50,000 = 30% of 3,50,000 = 1,05,000
Q = (45 – 30)% of 3,50,000 = 15% of 3,50,000 = 52,500
R = (65 – 45)% of 3,50,000 = 20% of 3,50,000 = 70,000
S = (75 – 65)% of 3,50,000 = 10% of 3,50,000 = 35,000
T = (90 – 75)% of 3,50,000 = 15% of 3,50,000 = 52,500
U = (100 – 90)% of 3,50,000 = 10% of 3,50,000 = 35,000.
In 2001: Total number of cars produced = 4,40,000.
P = (40 – 0)% of 4,40,000 = 40% of 4,40,000 = 1,76,000
Q = (60 – 40)% of 4,40,000 = 20% of 4,40,000 = 88,000
R = (75 – 60)% of 4,40,000 = 15% of 4,40,000 = 66,000
S = (85 – 75)% of 4,40,000 = 10% of 4,40,000 = 44,000
T = (95 – 85)% of 4,40,000 = 10% of 4,40,000 = 44,000
U = (100 – 95)% of 4,40,000 = 5% of 4,40,000 = 22,000
Now, we shall solve the questions.
Total number of cars of models P, Q and T manufactured in 2000
= (105000 + 52500 + 52500) = 2,10,000.
S7. Ans.(b)
Sol. Using the above calculation, the percentage change (rise/fall) in production from 2000 to 2001 for various model is:
∴ Minimum percentage rise/fall in production is in the case of model R.
S8. Ans.(a)
Sol. Required difference = 88000 – 52500 = 35500
S9. Ans.(b)
Sol. If the percentage production of P type cars in 2001 = percentage production of P type cars in 2000 = 30%
Then, number of P type cars produced in 2001 = 30% of 440000 = 132000.
S10. Ans.(c)
Sol. Number of S type cars which remained unsold in 2000 = 15% of 35000
and number of S type car which remained unsold in 2001 = 15% of 44000
∴ Total number of S type cars which remained unsold
= 15% of (35000 + 44000) = 15% of 79000 = 11850.
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