RD Sharma Solutions Class 7 Percentage Exercise 11.6

RD Sharma Solutions Class 7 Chapter 11 Exercise 11.6

RD Sharma Class 7 Solutions Chapter 11 Ex 11.6 PDF Free Download

Exercise 11.6

 Q1. Ashu had 24 pages to write. By the evening, he had completed 25% of his work. How many pages were left?

\(Total\;number\;of\;pages=24\\ Number\;of\;pages\;completed=25\%\;of\;24\;pages\\ =\frac{25}{100}\times24\\ =\frac{1}{4}\times24\\ =6\;pages\\ Therefore\;no\;of\;pages\;left= Total-Pages\;completed\\ =\left(24-6 \right )pages\\ =18\;pages\)

Q2. A box contains 60 eggs. Out of which \(16\frac{2}{3}\) % are rotten ones. How many eggs are rotten?

\(Total\;number\;of\;eggs=60\\ Number\;of\;eggs\;rotten=16\frac{2}{3}\%\;of\;60\;eggs\\ =16.66\%\;of\;60\;eggs\;\\ =\frac{16.66}{100}\times60\\ =10\;eggs\\ Therefore\;no\;of\;eggs\;rotten= 10\;eggs\;\)

Q3. Rohit obtained 45 marks out of 80. What per cent marks did he get?

\(Total\;number\;of\;marks=80\\ Rohit\;obtained=45\\ Required\;percentage=\frac{45}{80}\times100\\ =\frac{9}{16}\times100\\ =56.25\%\)

Q4. Mr Virmani saves 12% of his salary. If he receives Rs 15900 per month as salary, find his monthly expenditure.

\(Salary=Rs.15900\\ Savings=12\%\;of\;salary\\ =\frac{12}{100}\times\;15900\\ =Rs.1908\\ Therefore\;Expenditures= Salary-Savings\\ =Rs.15900-Rs.1908\\ =Rs.13992\)

Q5. A lawyer willed his 3 sons Rs 250000 to be divided into portions 30%, 45% and 25%. How much did each of them inherit?

\(Total\;amount=Rs.250000\\ Therefore\\ 30\%\;of\;amount=\frac{30}{100}\times250000\\ =30\times2500\\ =Rs.75000\\ 45\%\;of\;amount=\frac{45}{100}\times250000\\ =45\times2500\\ =Rs.112500 \\ 25\%\;of\;amount=\frac{25}{100}\times250000\\ =25\times2500\\ =Rs.62500\\ Therefore\;portions\;of\;amounts\;are\;Rs.75000,Rs.112500\;and\; Rs.62500\)

Q6. Rajdhani College has 2400 students, 40% of whom are girls. How many boys are there in the college?

\(Total\;number\;of\;students=2400\\ 40\%\;of\;2400=\frac{40}{100}\times\;2400\\ =40\times24\\ =960 girls\\ Therefore\;no\;of\;boys=Total\;students-girls\\ =2400-960\\ =1440\;boys\)

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?

\(Aman\;scored\;410\;marks\;out\;of\;500\\ =\frac{410}{500}\times100\\ =82\%\\ Anish\;scored\;536\;marks\;out\;of\;600\\ =\frac{536}{600}\times100\\ =89\%\\ Anish\;performance\;is\;better\)

Q8. Rahim obtained 60 marks out of 75 in Mathematics. Find the percentage of marks obtained by Rahim in Mathematics.

\(Total\;no\;of\;marks=75\\ Rahim\;obtained=60\\ Required\;percentage=\frac{60}{75}\times100\\ =80\%\)

Q9. In an orchard, \(16\frac{2}{3}\) % of the trees are apple trees. If the number of trees in the orchard is 240, 3 find the number of other type of trees in the orchard.

\(Total\;number\;of\;trees=240\\ Apple\;trees=16\frac{2}{3}\times\;240\\ =16.66\%\;of\;240\\ =\frac{16.66}{100}\times240\\ =40\;trees\\ No\;of\; trees\; other\; than\; apple\; tree=Total\;trees-apples\;trees\\ =240-40\\ =40\;trees\)

Q10. Ram scored 553 marks out of 700 and Gita scored 486 marks out of 600 in science. Whose performance is better?

\(Ram\;obtained\;553\;out\;of\;700\\ Ram\;percentage=\frac{553}{700}\times100\\ =\frac{553}{7}\\ =79\% Gita\;obtained\;486\;out\;of\;600\\ ita\;percentage=\frac{486}{600}\times100\\ =\frac{486}{6}\\ =81\%\\ Therefore\;Gita\;performance\;is\;better\)

Q11. Out of an income of Rs 15000, Nazima spends Rs 10200. What per cent of her income does she save?

\(Total\;income=Rs.15000\\ Savings=Income-Expenditure\\ =Rs.15000-Rs.10200\\ =Rs.4800\\ Percentage\;of\;income=\frac{4800}{15000}\times100\\=32\%\)

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.

\(Total \;number\; of \;students=880\\ number \;of \;boys=45\%\;of\;880\\ =\frac{45}{100}\times 880\\ =45\times8.8\\ =396boys\\ No\; of \;girls=Total\;students-no\; of\;boys\\ =880-396\\ =484\;girls\\ Therefore\;no\;of\;girls=484\;girls\\\)

Q13. Mr. Sidhana saves 28% of his income. If he saves As 840 per month, find his monthly income.

\(28\% of\; salary=Rs.840\\ Let\; the\; salary\; of\; Mr.Sidhana\;be\;x 28\%\;of\;x=840\\ x=\frac{840\times100}{28}\\ =Rs.3000\\ Therefore\;Mr.Sidhana\;salary\;is\;Rs.3000\)

 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?

\(Total \;no\; of \;students=1650\\ 8\% \;of\; students \;failed\\ Passed\; students\%=100\%-8\%\\ =92\%\\ Therefore\;number\; of \;students \;passed=92\%\;of \;1650\\ =\frac{92}{100}\times1650\\ =92\times16.5\\ =1518\\ Therefore\;1518\;students\;passed\)

Q15. In an examination, 92% of the candidates passed and 46 failed. How many candidates appeared?

\(92\%\; of\; students \;passed \;means\; 8\% \;students \;failed\\ Let\; the \;number\; of \;students\; be \;x \;then,\\ 8\%\; of \;x=46\\ x=\frac{46\times100}{8}\\= 575\\ Therefore\; total \;number\; of \;students=575\)

Practise This Question

On multiplying a decimal number by 100, we shift the decimal point  (i) ______  places to the  (ii) ______  and on dividing a decimal number by 100, we shift the decimal point,  (iii)_______  places to the  (iv) _______.