## 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.