Q1. Ashu had 24 pages to write. By the evening, he had completed 25 % of his work.How many pages were left?
Sol. Total mumber of pages =24
$$ \text {Number of pages completed } =25 \% \text { of } 24 =\frac{25}{100} \times 24 $$ $$ =\frac{1}{4} \times 24 $$ =6 pages. Therefore, no. of pages left = 24 – 6 = 18 pages.\begin{array}{l} \text {Q2. A box contains 60 eggs. Out of which } 16 \frac{2}{3} \% \text { are rotten ones. How many eggs are rotten? } \end{array}Sol. Total mumber of eggs =60
$$ \text {Number of eggs rotten } =16 \frac{2}{3} \% \text { of } 60 $$ $$ =\frac{50}{3 \times 100} \times 60 $$ =10 eggs
Therefore, there are 10 rotten eggs.
Q3. Rohit obtained 45 marks out of 80. What per cent marks did he get?
Sol. Total number of marks =80
Rohit obtained = 45
$$ \text {Req. percentage}=\frac{45}{80} \times 100 $$ $$ =\frac{9}{16} \times 100 $$ $$ =56 \frac {1}{4} \% $$Q4. Mr Virmani saves 12 % of his salary. If he receives Rs 15900 per month as salary, find his monthly expenditure.
Sol. Given Salary Rs. }=15900
$$ \text {Savings } =12 \% \text { of salary } =\frac{12}{100} \times 15900 $$ =Rs. 1908
Therefore, Expenditure = Salary – Savings = 15900 – 1908 =Rs. 13992
Q5. A lawyer willed his 3 sons Rs. 250000 to be divided into portions 30%, 45% and 25%. How much did each of them innerit?
Sol.Total amount =Rs. 250000
$$ 30 \% \text { of amount }=\frac{30}{100} \times 250000 $$ $$ =30 \times 2500=\text {Rs. } 75000 $$$$ 45 \% \text { of amount } =\frac{45}{100} \times 250000 $$ $$ =45 \times 2500 =\text {Rs. } 112500 $$$$ 25 \% \text { of amount } =\frac{25}{100} \times 250000 $$ $$ =25 \times 2500=\text {Rs. } 62500 $$ Therefore, Portions of amounts are Rs. 75000, Rs. 112500 and Rs. 62500
Q6. Rajohani College has 2400 students, 40% of whom are girls. How many boys are there in the college?
Sol. Total mumber of students = 2400
$$ \text {Girls students } 40 \% \text { of } 2400=\frac{40}{100} \times 2400 =40 \times 24 =960 $$Therefore, no.of boys students= Total students – Girl students = 2400 – 960 = 1440
Q7. Aman obtained 410 marks out of 500 in CBSE XII examination while his brother Anish gets 536 marks out of 600 in IX class examination. Find whose performance is better?
Sol. Aman scored 410 marks out of 500
$$ =\frac{410}{500} \times 100 \% =82 \% $$$$ \text {Anish scored 536 marks out of 600} =\frac{536}{600} \times 100 \% =89 \% $$ Therefore, Anish’s performance is better.
Q8. Rahim obtained 60 marks out of 75 in Mathematics. Find the percentage of marks obtained by Rahim in Mathematics.
Sol. Total no. of marks = 75
Rahim obtained = 60
$$ \text {Req. percentage}=\frac{60}{75} \times 100 \%=80 \% $$$$ \text {Q9. In an orchard, } 16 \frac{2}{3} \% \text { of the trees are apple trees.} $$ If the number of trees in the orchard is 240 find the number of other type of trees in the orchard.
Sol. Total number of trees =240
$$ \text {Apple trees}=16 \frac{2}{3} \times 240 =40 $$No. of trees other than apple tree = Total trees – Apple trees = 240 – 40 = 40 treesQ10. Ram scored 553 marks out of 700 and Gita scored 486 marks out of 600 in science. Whose performance is better?
Sol. Ram obtained 553 out of 700.
$$ \text {Ram percentage} =\frac{553}{700} \times 100 =\frac{553}{7}=79 \% $$ Gita obtained 486 out of 600.
$$ \text {Gita percentage}=\frac{486}{600} \times 100 =\frac{486}{6} =81 \% $$ Therefore, Gita’s performanceis better.
Q11. Out of an income of Rs 15000, Nazima spends Rs 10200. What per cent of her income does she save?
Sol. Total income = Rs. 15000
Savings = Income – Expenditure = 15000 – 10200 = Rs. 4800
$$ \text {Saving percentage} =\frac{4800}{15000} \times 100 =32 \% $$Q12. 45% of the students in a school are boys. If the total number of students in the school is 880 find the number of girls in the school.
Sol. Total number of students = 880
$$ \text {Number of boys } =45 \% \text { of } 880 $$ $$ =\frac{45}{100} \times 880 $$ $$ =9 \times 44=396 $$ Therefore, No. of girls = Total students – No. of boys = 880 – 396 =484
Q13. Mr. Sidhana saves 28% of his income. If he saves Rs 840 per month, find his monthly income.
Sol. Let the salary of Mr. Sidhana be x.
According to question, 28% of salary =840
$$ \Rightarrow \quad 28 \% \text { of } x=840 $$ $$ \Rightarrow \quad \frac {28}{100} \times x=840 $$ $$ \Rightarrow \quad x=\frac{840 \times 100}{28} $$ $$ \Rightarrow \quad x =3000 $$ Therefore, Mr. Sidhana salary is Rs. 3000.
Q14. In an examination, 8% of the students fail. What percentage of the students pass? If 1650 students appeared in the examination, how many passed?
Sol. Total no.of students =1650
8% of students failed. Therefore, passed students percentage =100 – 8 =92%
Number of students passed =92% of 1650
$$ =\frac{92}{100} \times 1650 = 1518 $$Q15. In an examination, 92% of the candidates passed and 46 failed. How many candidatess appeared?
Sol. Given that 92% of students passed. It means 100-92 =8% students failed.
Let’s assume that total mumber of students be x, then
$$ 8 \% \text { of } x = 46 $$ $$ \Rightarrow \quad \frac {8}{100} \times x = 46 $$ $$ \Rightarrow \quad x=\frac{46 \times 100}{8} $$ $$ \Rightarrow \quad x =575 $$ Therefore, a total of 575 candidates appeared in the examination.
Sol. Total mumber of pages =24
$$ \text {Number of pages completed } =25 \% \text { of } 24 =\frac{25}{100} \times 24 $$ $$ =\frac{1}{4} \times 24 $$ =6 pages. Therefore, no. of pages left = 24 – 6 = 18 pages.\begin{array}{l} \text {Q2. A box contains 60 eggs. Out of which } 16 \frac{2}{3} \% \text { are rotten ones. How many eggs are rotten? } \end{array}Sol. Total mumber of eggs =60
$$ \text {Number of eggs rotten } =16 \frac{2}{3} \% \text { of } 60 $$ $$ =\frac{50}{3 \times 100} \times 60 $$ =10 eggs
Therefore, there are 10 rotten eggs.
Q3. Rohit obtained 45 marks out of 80. What per cent marks did he get?
Sol. Total number of marks =80
Rohit obtained = 45
$$ \text {Req. percentage}=\frac{45}{80} \times 100 $$ $$ =\frac{9}{16} \times 100 $$ $$ =56 \frac {1}{4} \% $$Q4. Mr Virmani saves 12 % of his salary. If he receives Rs 15900 per month as salary, find his monthly expenditure.
Sol. Given Salary Rs. }=15900
$$ \text {Savings } =12 \% \text { of salary } =\frac{12}{100} \times 15900 $$ =Rs. 1908
Therefore, Expenditure = Salary – Savings = 15900 – 1908 =Rs. 13992
Q5. A lawyer willed his 3 sons Rs. 250000 to be divided into portions 30%, 45% and 25%. How much did each of them innerit?
Sol.Total amount =Rs. 250000
$$ 30 \% \text { of amount }=\frac{30}{100} \times 250000 $$ $$ =30 \times 2500=\text {Rs. } 75000 $$$$ 45 \% \text { of amount } =\frac{45}{100} \times 250000 $$ $$ =45 \times 2500 =\text {Rs. } 112500 $$$$ 25 \% \text { of amount } =\frac{25}{100} \times 250000 $$ $$ =25 \times 2500=\text {Rs. } 62500 $$ Therefore, Portions of amounts are Rs. 75000, Rs. 112500 and Rs. 62500
Q6. Rajohani College has 2400 students, 40% of whom are girls. How many boys are there in the college?
Sol. Total mumber of students = 2400
$$ \text {Girls students } 40 \% \text { of } 2400=\frac{40}{100} \times 2400 =40 \times 24 =960 $$Therefore, no.of boys students= Total students – Girl students = 2400 – 960 = 1440
Q7. Aman obtained 410 marks out of 500 in CBSE XII examination while his brother Anish gets 536 marks out of 600 in IX class examination. Find whose performance is better?
Sol. Aman scored 410 marks out of 500
$$ =\frac{410}{500} \times 100 \% =82 \% $$$$ \text {Anish scored 536 marks out of 600} =\frac{536}{600} \times 100 \% =89 \% $$ Therefore, Anish’s performance is better.
Q8. Rahim obtained 60 marks out of 75 in Mathematics. Find the percentage of marks obtained by Rahim in Mathematics.
Sol. Total no. of marks = 75
Rahim obtained = 60
$$ \text {Req. percentage}=\frac{60}{75} \times 100 \%=80 \% $$$$ \text {Q9. In an orchard, } 16 \frac{2}{3} \% \text { of the trees are apple trees.} $$ If the number of trees in the orchard is 240 find the number of other type of trees in the orchard.
Sol. Total number of trees =240
$$ \text {Apple trees}=16 \frac{2}{3} \times 240 =40 $$No. of trees other than apple tree = Total trees – Apple trees = 240 – 40 = 40 treesQ10. Ram scored 553 marks out of 700 and Gita scored 486 marks out of 600 in science. Whose performance is better?
Sol. Ram obtained 553 out of 700.
$$ \text {Ram percentage} =\frac{553}{700} \times 100 =\frac{553}{7}=79 \% $$ Gita obtained 486 out of 600.
$$ \text {Gita percentage}=\frac{486}{600} \times 100 =\frac{486}{6} =81 \% $$ Therefore, Gita’s performanceis better.
Q11. Out of an income of Rs 15000, Nazima spends Rs 10200. What per cent of her income does she save?
Sol. Total income = Rs. 15000
Savings = Income – Expenditure = 15000 – 10200 = Rs. 4800
$$ \text {Saving percentage} =\frac{4800}{15000} \times 100 =32 \% $$Q12. 45% of the students in a school are boys. If the total number of students in the school is 880 find the number of girls in the school.
Sol. Total number of students = 880
$$ \text {Number of boys } =45 \% \text { of } 880 $$ $$ =\frac{45}{100} \times 880 $$ $$ =9 \times 44=396 $$ Therefore, No. of girls = Total students – No. of boys = 880 – 396 =484
Q13. Mr. Sidhana saves 28% of his income. If he saves Rs 840 per month, find his monthly income.
Sol. Let the salary of Mr. Sidhana be x.
According to question, 28% of salary =840
$$ \Rightarrow \quad 28 \% \text { of } x=840 $$ $$ \Rightarrow \quad \frac {28}{100} \times x=840 $$ $$ \Rightarrow \quad x=\frac{840 \times 100}{28} $$ $$ \Rightarrow \quad x =3000 $$ Therefore, Mr. Sidhana salary is Rs. 3000.
Q14. In an examination, 8% of the students fail. What percentage of the students pass? If 1650 students appeared in the examination, how many passed?
Sol. Total no.of students =1650
8% of students failed. Therefore, passed students percentage =100 – 8 =92%
Number of students passed =92% of 1650
$$ =\frac{92}{100} \times 1650 = 1518 $$Q15. In an examination, 92% of the candidates passed and 46 failed. How many candidatess appeared?
Sol. Given that 92% of students passed. It means 100-92 =8% students failed.
Let’s assume that total mumber of students be x, then
$$ 8 \% \text { of } x = 46 $$ $$ \Rightarrow \quad \frac {8}{100} \times x = 46 $$ $$ \Rightarrow \quad x=\frac{46 \times 100}{8} $$ $$ \Rightarrow \quad x =575 $$ Therefore, a total of 575 candidates appeared in the examination.