Directions Q (1-5):- A soft-drink company prepares drinks of three different falvours – X, Y and Z. The production of the three falvours 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.
1. For which of the following years the percentage of rise /fall in production from the previous year is the maximum for the falvour Y?
(a) 1996 (b) 1997
(c) 1998 (d) 1999
(e) 2000
2. For which falvour 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
3. The total production of falvour Z in 1997 and 1998 is what percentage of the total production falvour X in 1995 and 1996?
(a) 96.67% (b) 102.25%
(c) 115.57% (d) 120%
(e) 133.33%
4. What is the difference between the average production of falvour X in 1995, 1996 and 1997 and the average production of falvour 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
5. What was the approximate decline in the production of falvour Z in 2000 as compared to the production in 1998?
(a) 50% (b) 42%
(c) 33% (d) 25%
(e) 22.5%
Directions Q (6-10):- In a school the periodical examinations are held every second month. IN a session during Apr. 2001 – Mar. 2002, a student of Class IX appeared for each of the periodical exams. The aggregate marks obtained by him in each periodical exam are represented in the line –
Graph given below. Study the graph and answer the questions based on it.
MARKS OBTAINED BY A STUDENT IN SIX PERIODICAL EXAMS HELD IN EVERY TWO MONTHS DURING THE YEAR IN THE SESSION 2001 – 02
6. The total number of marks obtained in Feb. 02 is what percent of the total marks obtained in Apr. 01?
(a) 110% (b) 112.5%
(c) 115% (d) 116.5%
(e) 117.5%
7. What are the average marks obtained by the student in all the periodical exams during the session?
(a) 373 (b) 379
(c) 381 (d) 385
(e) 389
8. What is the percentage of marks obtained by the student in the periodical exams of Aug. 01 and Oct. 01 taken together?
(a) 73.25% (b) 75.5%
(c) 77% (d) 78.75%
(e) 79.5%
9. In which periodical exams there is a fall in percentage of marks as compared to the previous periodical exams?
(a) None (b) Jun. 01
(c) Oct. 01 (d) Dec. 01
(e) Feb. 02
10. In which periodical exams did the student obtain the highest percentage increase in marks over the previous periodical exams?
(a) Jun. 01 (b) Aug. 01
(c) Oct. 01 (d) Dec. 01
(e) Feb. 02
ANSWER:
1. | (b) |
2. | (b) |
3. | (e) |
4. | (e) |
5. | (c) |
6. | (b) |
7. | (c) |
8. | (b) |
9. | (a) |
10. | (c) |
ANSWER WITH SOLUTION:
1. The percentage rise/fall in production from the previous year for flavour Y during various years are:
In 1996 = [ {(60-55) /55} * 100]% = 9.09% (raise)
In 1997 = [ {(60-50) /60} * 100]% = 16.67% (fall)
In 1998 = [ {(55-50) /50} * 100]% = 10% (raise)
In 1999 = [ {(55-50) /55} * 100]% = 9.09% (fall)
In 2000 = [ {(55-50) /50} * 100]% = 10% (raise)
So, Maximum change is decrease of 16.67% during 1997.
2. Average annual productions over the given period for various flavours are:
For falvour X= [1/6 * (50+40+55+45+60+50)] lakh bottles = 50 lakh bottles.
For falvour Y= [1/6 * (55+60+50+55+50+55)] lakh bottles = 54.17 lakh bottles.
For falvour Z= [1/6 * (45+50+60+60+45+40)] lakh bottles = 50 lakh bottles.
So maximum average production is for falvour Y.
3. Required percentage =[{(60+60) /(50+40)} * 100] % = (120/90 *100)% = 133.33%
4. Average production of falvour X in 1995, 1996 and 1997 = [1/3 * (50+40+55)] lakh bottles
= (145/3) lakh bottles
Average production of falvour Y in 1998, 1999 and 2000 = [1/3 * (55+50+55)] lakh bottles
= (160/3) lakh bottles
So difference = (160/3 – 145/3) = 15/3 = 5 lakh bottles= 5,00,000 bottles
5. Percentage decline in the production of flavor Z in 2000 as compared to the production in 1998 =
=[{(60-40)/60} * 100] % =(20/60 *100)%= 33.33%= 33%
6. Required percentage = ={(405/ 360) * 100} % = 112.5%
7. Average marks obtained in all the periodical exams = = 1/6 *[360+365+370+385+400+405] = 380.83 =381
8. Required percentage = [{(370+385)/ (500+500)} * 100] % = (755/1000) * 100 %= 75.5%
9. As it is clear from the graph, the total marks obtained in periodical exams, go on increasing. Since the maximum marks for all the periodical exams are same, it implies that the percentage of mars also goes on increasing. Thus, in none of the periodical exams, there is a fall in percentage of marks compared to the previous exam.
10. Percentage increase in marks in various periodical exams compared to the previous exams are :
For Jun 01 = [ {(365-360) /360} * 100]% = 1.39%
For Aug 01= [ {(370-365) /365} * 100]% = 1.37%
For Oct 01 = [ {(385-370) /370} * 100]% = 4.05%
For Dec 01= [ {(400-385) /55} * 100]% = 3.90%
For Feb 02 = [ {(405 -400) /400} * 100]% = 10%
Clearly, highest percentage increase in marks is in Oct 01.
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