Percentage - Arithmetic

Question (1) In an examination, 90% of students passed and 1070 failed. If there were 70% boys among students who passed, then find the total number of girls among students who passed and the total number of students who appeared in the examination.

Solution

Given, percent of students passed = 90%

Number of students failed = 1070

Percentage of boys among students who passed = 70%

Thus, total number of students and number of girls among students who passed = ?

Calculation of total number of students who appeared in the examination

Here, since 90% students passed

Thus, fail% = 100 – 90 = 10%

Now, ∵ 10% = 1070

∴ 100% = 1070 × 10

[Since, 10 × 10 = 100, thus 100% = 1070 × 10]

∴ 100% = 10700

Thus, total number of students appeared in the examination = 10700

Calculation of total number of students among students who passed

Now, number of students who failed = 1070

Thus, number of students among students who passed = Total number of students – Number of students who failed

= 10700 – 1070

= 9630

Thus, total number of students who passed = 9630

Calculation of number of girls among students who passed

Now, as given percentage of boys among students who passed = 70%

Thus, percentage of girls among students who passed = 100 – 70 = 30%

Thus, the number of girls among students who passed = 30% of Total number of students who passed

= 30% of 9630

= 3 × 963

= 2889

Thus, total number of girls who passed = 2889

Thus, total number of students who appeared is 10700 and number of girls among students who passed = 2889 Answer

Question (2) In an examination, 95% of students passed and 535 failed. If there were 40% boys among students who passed, then find the total number of girls among students who passed and the total number of students who appeared in the examination.

Solution

Given, percent of students passed = 95%

Number of students failed = 535

Percentage of boys among students who passed = 40%

Thus, total number of students and number of girls among students who passed = ?

Calculation of total number of students who appeared in the examination

Here, since 95% students passed

Thus, fail% = 100 – 95 = 5%

Now, ∵ 5% = 535

∴ 100% = 535 × 20

[Since, 5 × 20 = 100, thus 100% = 535 × 20]

∴ 100% = 10700

Thus, total number of students appeared in the examination = 10700

Calculation of total number of students who passed

Now, number of students who failed = 535

Thus, number of students who passed = Total number of students – Number of students who failed

= 10700 – 535

= 10165

Thus, total number of students who passed = 10165

Calculation of number of girls among students who passed

Now, as given percentage of boys among students who passed = 40%

Thus, percentage of girls among students who passed = 100 – 40 = 60%

Thus, the number of girls among students who passed = 60% of the total number of students who passed

= 60% of 10165

= 0.6 × 10165

= 6099

Thus, total number of girls among students who passed = 6099

Thus, total number of students who appeared is 10700 and number of girls who passed = 6099 Answer

Question (3) In an examination, 80% of students passed and 190 failed. If there were 20% boys among students who passed, then find the total number of girls among students who passed and the total number of students who appeared in the examination.

Solution

Given, percent of students passed = 80%

Number of students failed = 190

Percentage of boys among students who passed = 20%

Thus, total number of students and number of girls among students who passed = ?

Calculation of total number of students who appeared in the examination

Here, since 80% students passed

Thus, fail% = 100 – 80 = 20%

Now, ∵ 20% = 190

∴ 100% = 190 × 20

[Since, 20% × 5% = 100%, thus 100% = 190 × 5]

∴ 100% = 950

Thus, total number of students appeared in the examination = 950

Calculation of total number of students who passed

Now, number of students who failed = 190

Thus, number of students who passed = Total number of students – Number of students who failed

= 950 – 190

= 760

Thus, total number of students who passed = 760

Calculation of number of girls among students who passed

Now, as given percentage of boys among students who passed = 20%

Thus, percentage of girls among students who passed = 100 – 20 = 80%

Thus, the number of girls among students who passed = 80% of the total number of students who passed

= 80% of 760

= 8 × 76

= 608

Thus, total number of girls among students who passed = 608

Thus, total number of students who appeared is 950 and number of girls who passed = 608 Answer

Question (4) In an examination, 75% of students passed and 5000 failed. If there were 55% boys among students who passed, then find the total number of girls among students who passed and the total number of students who appeared in the examination.

Solution

Given, percent of students passed = 75%

Number of students failed = 5000

Percentage of boys among students who passed = 55%

Thus, total number of students and number of girls among students who passed = ?

Calculation of total number of students who appeared in the examination

Here, since 75% students passed

Thus, fail% = 100 – 75 = 25%

Now, ∵ 25% = 5000

∴ 100% = 5000 × 4

[Since, 25% × 4% = 100%, thus 100% = 500 × 4]

∴ 100% = 20000

Thus, total number of students appeared in the examination = 20000

Calculation of total number of students who passed

Now, number of students who failed = 5000

Thus, number of students who passed = Total number of students – Number of students who failed

= 20000 – 5000

= 15000

Thus, total number of students who passed = 15000

Calculation of number of girls among students who passed

Now, as given percentage of boys among students who passed = 55%

Thus, percentage of girls among students who passed = 100% – 55% = 45%

Thus, the number of girls among students who passed = 80% of the total number of students who passed

= 45% of 15000

= 45 × 150

= 6750

Thus, total number of girls among students who passed = 6750

Thus, total number of students who appeared is 20000 and number of girls who passed = 6750 Answer