Chapter 12 – Percentage
Practice set 30
Solve the following.
(1) Shabana scored 736 marks out of 800 in her exams. What was the percentage she scored?
Solution:
Total marks of the examination = 800
Marks scored by Shabana = 736
Let Shabana scored A% marks.
\(\large \frac {A}{100}\) = \(\large \frac {736}{800}\)
∴ \(\large \frac {A}{100}\) × 100 = \(\large \frac {736}{800}\) × 100 …(Multiplying both sides by 100)
∴ A = \(\large \frac {736\,×\,100}{800}\)
∴ A = \(\large \frac {736}{8}\)
∴ A = 92%
Ans: Shabana scored 92% marks.
(2) There are 500 students in the school in Dahihanda village. If 350 of them can swim, what percent of them can swim and what percent cannot?
Solution:
Total number of students in the school = 500
Number of students who can swim = 350
Let A% students can swim.
\(\large \frac {A}{100}\) = \(\large \frac {736}{800}\)
∴ \(\large \frac {A}{100}\) × 100 = \(\large \frac {350}{500}\) × 100 …(Multiplying both sides by 100)
∴ A = \(\large \frac {350\,×\,100}{500}\)
∴ A = \(\large \frac {350}{5}\)
∴ A = 70%
Percentage of students who cannot swim
= 100% – Percentage of students who can swim
= 100% – 70%
= 30%
Ans: 70% of the students can swim and 30% cannot swim.
(3) If Prakash sowed jowar on 75% of the 19500 sq m of his land, on how many sq m did he actually plant jowar?
Solution:
Total area of the land = 19500 sq. m.
Percentage of area in which Prakash sowed jowar = 75%
Let Prakash planted jowar in A sq. m.
\(\large \frac {A}{19500}\) = \(\large \frac {75}{100}\)
∴ \(\large \frac {A}{19500}\) × 19500 = \(\large \frac {75}{100}\) × 19500 …(Multiplying both sides by 19500)
∴ A = \(\large \frac {75\,×\,19500}{100}\)
∴ A = 75 × 195
∴ A = 14,625 sq. m.
Ans: Prakash planted jowar in 14,625 sq.m.
(4) Soham received 40 messages on his birthday. Of these, 90% were birthday greetings. How many other messages did he get besides the greetings?
Solution:
Total messages received by Soham on his birthday = 40
Percentage of messages received for birthday greetings = 90%
Let Soham got A number of birthday greetings.
\(\large \frac {A}{40}\) = \(\large \frac {90}{100}\)
∴ \(\large \frac {A}{40}\) × 40 = \(\large \frac {90}{100}\) × 40 …(Multiplying both sides by 40)
∴ A = \(\large \frac {90\,×\,40}{100}\)
∴ A = 9 × 4
∴ A = 36
Number of messages received other than birthday greetings
= Total messages received – total number of birthday greetings
= 40 – 36
= 4
Ans: The number of messages received other than birthday greetings is 4.
(5) Of the 5675 people in a village 5448 are literate. What is the percentage of literacy in the village?
Solution:
Number of people in the village = 5675
Number of people who are literate = 5448
Let the percentage of literacy in the village is A%.
\(\large \frac {A}{100}\) = \(\large \frac {5448}{5675}\)
∴ \(\large \frac {A}{100}\) × 100 = \(\large \frac {5448}{5675}\) × 100 …(Multiplying both sides by 100)
∴ A = \(\large \frac {5448\,×\,100}{5675}\)
∴ A = 96%
Ans: The percentage of literacy in the village is 96%.
(6) In the elections, 1080 of the 1200 women in Jambhulgaon cast their vote, while 1360 of the 1700 in Wadgaon cast theirs. In which village did a greater proportion of women cast their votes?
Solution:
Total number of women in Jambhulgaon = 1200
Number of women in Jambhulgaon who voted = 1080
Let A% women cast their vote in Jambhulgaon village.
\(\large \frac {A}{100}\) = \(\large \frac {1080}{1200}\)
∴ \(\large \frac {A}{100}\) × 100 = \(\large \frac {1080}{1200}\) × 100 …(Multiplying both sides by 100)
∴ A = \(\large \frac {1080\,×\,100}{1200}\)
∴ A = \(\large \frac {1080}{12}\)
∴ A = 90%
In Jambhulgaon, the percentage of women who voted in the elections was 90%.
Total number of women in Wadgaon = 1700
Number of women in Wadgaon who voted = 1360
Let B% women cast their vote in Wadgaon.
\(\large \frac {B}{100}\) = \(\large \frac {1360}{1700}\)
∴ \(\large \frac {B}{100}\) × 100 = \(\large \frac {1360}{1700}\) × 100 …(Multiplying both sides by 100)
∴ B = \(\large \frac {1360\,×\,100}{1700}\)
∴ B = \(\large \frac {1360}{17}\)
∴ B = 80%
In Wadgaon, the percentage of women who voted in the elections was 80%.
A% > B%
Ans: A greater proportion of women cast their votes in Jambhulgaon.