11. Two candidates contested an election. The losing candidate got 40% votes and lost by 2000 votes. Find the total number of votes cast.
a. 5000
b. 8000
c. 10000
d. 20000
1st candidate lost by 1000 votes = difference of votes between both candidates
∴ a = 10,000.
12. Present population of a city is 60,000. It increases at the rate of 10%. Find the population of the city after 4 years.
a. 65,550
b. 80,500
c. 87,846
d. 88,550
Using formula given above -
13. Ram grew up in a small city with population 40,000 in 1982. He remembers that the census at the end of 1983 said that the population has increased by 25% but due to an epidemic, the population fell down by 30% in 1984. In 1985 there was an increase of 40% in the population. Find the population of the city at the end of 1985.
a. 70250
b. 72250
c. 76550
d. 73500
Using formula given above -
Rate 1 = R1 = 25% (increase);
Rate 2 = R2 = 30% (decrease);
Rate 3 = R3 = 40% (increase)
= 73,500
14. A Principal wanted to improve the performance of her school in languages and asks for annual report from teachers, Filing the annual report for Class V, a teacher commented, 15% of students failed in English, 25% of students failed in Hindi while 10% of students failed in both the subjects. What percentage of students passed in both the subjects English and Hindi?
a. 60%
b. 70%
c. 80%
d. 90%
Percentage of students who passed in both subjects = (100 - 30) % = 70%
Thus, 70% passed in both subjects.
15. The monthly finance tracker of a person reads as below
Savings for the month : Rs 7200/-
Find the amount he spent on travel that month.
a. Rs. 7000
b. Rs. 7100
c. Rs. 7200
d. Rs. 7300
a. 5000
b. 8000
c. 10000
d. 20000
Answer: c. 10000
Explanation:
Total votes = a.
This means that, Votes of candidate 1 + Votes of candidate 2 = a
| We know that, Votes of candidate 1 = 40% of a = | 40a |
| 100 |
| Hence, Votes of candidate 2 = (100% - 40%) of a = 60% of a = | 60a |
| 100 |
| ∴ | 60a | - | 40a | = 2000 |
| 100 | 100 |
12. Present population of a city is 60,000. It increases at the rate of 10%. Find the population of the city after 4 years.
a. 65,550
b. 80,500
c. 87,846
d. 88,550
Answer: c. 87,846
Explanation:
Tip:
Remember this formula. It is similar to formula for COMPOUND INTEREST.
P = Population; R = Rate of increase or decrease; n = number of years;
'+' = during increase; '-' = during decrease
Remember this formula. It is similar to formula for COMPOUND INTEREST.
| Population after n years = P |  | 1 ± | R |  | n |
| 100 |
'+' = during increase; '-' = during decrease
Using formula given above -
| Population after 4 years = 60,000 | | 1 + | 10 | | 4 |
| 100 |
| = | 60,000 x 11 x 11 x 11 x 11 | = 87,846 |
| 10 x 10 x 10 x 10 |
13. Ram grew up in a small city with population 40,000 in 1982. He remembers that the census at the end of 1983 said that the population has increased by 25% but due to an epidemic, the population fell down by 30% in 1984. In 1985 there was an increase of 40% in the population. Find the population of the city at the end of 1985.
a. 70250
b. 72250
c. 76550
d. 73500
Answer: d. 73500
Explanation:
Tip:
Remember this formula. It is similar to formula for COMPOUND INTEREST.
P = Population; R = Rate of increase or decrease; n = number of years;
'+' = during increase; '-' = during decrease
Remember this formula. It is similar to formula for COMPOUND INTEREST.
| Population after n years = P | | 1 ± | R | | n |
| 100 |
'+' = during increase; '-' = during decrease
Using formula given above -
Rate 1 = R1 = 25% (increase);
Rate 2 = R2 = 30% (decrease);
Rate 3 = R3 = 40% (increase)
| Population after 3 years = 60,000 |  | 1 + | 25 |  | | 1 - | 30 | | | 1 + | 40 | |
| 100 | 100 | 100 |
| = 60,000 | | 125 | | | 70 | | | 140 | |
| 100 | 100 | 100 |
14. A Principal wanted to improve the performance of her school in languages and asks for annual report from teachers, Filing the annual report for Class V, a teacher commented, 15% of students failed in English, 25% of students failed in Hindi while 10% of students failed in both the subjects. What percentage of students passed in both the subjects English and Hindi?
a. 60%
b. 70%
c. 80%
d. 90%
Answer: b. 70%
Explanation:
Usual Mistake: Percentage of Students failing in both subjects = 25% + 15% = 40%
But as shown in the below diagram, the students who failed both subjects (10%) are counted twice - Once in 15% (blue circle) and once again in 25% (orange circle).
We need to subtract this double counting.
So students who failed subjects would be = 25% + 15% - 10% = 30%
Remember:
Subtract only once, not twice!
Percentage of students who passed in both subjects = (100 - 30) % = 70%
Thus, 70% passed in both subjects.
15. The monthly finance tracker of a person reads as below
| Item | Expenses out of income |
|---|---|
| Food | 30% |
| House Rent | 35% |
| Travel | 9% |
| Education | 17% |
Savings for the month : Rs 7200/-
Find the amount he spent on travel that month.
a. Rs. 7000
b. Rs. 7100
c. Rs. 7200
d. Rs. 7300
Answer: c. Rs. 7200
