Comparing Quantities - Worksheets

CBSE Worksheet-1
Class 08 - Mathematics (Comparing quantities)

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General Instructions: All questions are compulsory. Q.1 to Q.2 carries one mark each. Q.3 to Q.7 carries two marks each. Q.8 and Q.9 carries three marks each. Q.10 to Q.12 carries four marks each.

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1. A player won 70% of the cricket matches whenever he was in the team. In his total career, he lost 45 matches. How many matches he played overall?
2. If 8.5%of a number is 51, then find the number.
3. State whether the following statements are True/False:
   1. If a discount is given on an item, Sales Tax is calculated on the discounted price.
   2. The charges paid extra to the S.P. of an article is called over head expenses.
   3. The C.P. of an article whose S.P. is ₹150 at a gain of 50% is ₹ 100.
   4. The amount paid for an item costing ₹ 100 with 8% discount is ₹ 108.
4. Fill in the blanks:
   1. If S.P < C.P, then it is ____________.
   2. If S.P > C.P, then it is ____________.
   3. C.P – S.P = _____________.
   4. S.P. – C.P = ____________.
5. Match the following:

   Column A	Column B
   (a) 100×Gain Gain%$\frac{100\times Gain}{Gain\mathrm{\%}}$	(p) Gain%
   (b) 100+gain%100×C.P$\frac{100+gain\mathrm{\%}}{100}\times C.P$	(q) C.P.
   (c) GainC.P×100$\frac{Gain}{C.P}\times 100$	(r) Loss%
   (d) lossC.P×100$\frac{loss}{C.P}\times 100$	(s) S.P.

6. Find selling price (SP) if a profit of 5% is made on a lawn mower bought at Rs. 1150 with Rs. 50 as transportation charges.
7. Find interest and amount to be paid on Rs. 15000 at 5% per annum after 2 years.
8. A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then how many matches did they play in all ?
9. Find the Simple Interest and amount on ₹ 5000 for 6 months at the rate of 5% per annum.
10. A farmer buys a plot of agricultural land for ₹ 4, 50,000. He sells one-third at a loss of 15% and two-fifth at a gain of 20%. At what price must he sell the remaining land, so as to make an overall profit of 10%?
11. If 60% people in a city like cricket, 30% like football and the remaining like other games, then what per cent of the people like other games? If the total number of people are 50 lakh, find the exact number who like each type of game.
12. Maria invested Rs. 8000 in a business. She would be paid interest at rate of 5% per annum compounded annually. Find (i) the amount credited against her name at the end of the second year. (ii) the interest for the 3rd year.

CBSE Worksheet-1
Class 08 - Mathematics (Comparing quantities)
Solution

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1. Percentage of matches won = 70%
   Percentage of matches lost = 30%
   Let total matches played be x
   So, 30% of x = 45
   ⇒30100×x=45$\Rightarrow \frac{30}{100}\times x=45$
   ⇒x=45×10030=150$\Rightarrow x=\frac{45\times 100}{30}=150$
2. Let the number be x.
   Then, 8.5% of x = 51
   i.e., 8510%$\frac{85}{10}\mathrm{\%}$ of x = 51
   8510×1100×x=51$\frac{85}{10}\times \frac{1}{100}\times x=51$
   x=51×100×1085=600$x=\frac{51\times 100\times 10}{85}=600$
3. 1. True
   2. False, it is called Sales Tax.
   3. True, Let C.P of the article = ₹.x; S.P. = ₹ 150 ; Gain% = 50% ; Gain = 50% of ₹.x=₹.x2;$\frac{x}{2};$
      Gain = S.P - C.P. = ₹.150 - ₹.x =x2$=\frac{x}{2}$
      150=x2+x=3x2→x=2×1503=100;$150=\frac{x}{2}+x=\frac{3x}{2}\to x=\frac{2\times 150}{3}=100;$
      C.P. of the article = ₹100.
   4. False, 100 – 8 = ₹ 92 should be the amount paid for the item.
4. a. Loss, b. Profit, c. Loss, d. Profit
5. a. C.P., b. S.P., c. Gain%, d. Loss%
6. CP = Rs. 1150 + Rs. 50 = Rs. 1200
   Profit = 5% of Rs. 1200
   =Rs.5100×1200$=Rs.\frac{5}{100}\times 1200$ = Rs. 60
   ∴ SP = CP + Profit
   = Rs. 1200 + Rs. 60 = Rs. 1260
7. ∴ Interest on Rs. 100 for 1 year is = Rs. 5
   ∴ Interest on Rs. 15000 for 1 year is = Rs. 5100×15000$\frac{5}{100}\times 15000$
   ∴ Interest on Rs. 15000 for 2 years is = Rs.5×15000×2100$\frac{5\times 15000\times 2}{100}$
   = Rs. 1500
   ∴ Amount = Principle + Interest
   = Rs. 15000 + Rs. 1500 = Rs. 16500
8. Let the total number of matches be x.
   According to question,
   40% of total matches = 10
   ⇒$\Rightarrow$ 40% of x = 10
   ⇒40100×x=10$\Rightarrow \frac{40}{100}\times x=10$
   ⇒x=10×10040=25$\Rightarrow x=\frac{10\times 100}{40}=25$
   Hence, 25 matches were played in all.
9. Principal (P) = ₹ 5000
   Time period (T) = 6 months = 12$\frac{1}{2}$ year
   Rate of interest (R) = 5% p.a.
   Simple interest (S.I.) =P×T×R100=5000×1×52×100=₹125$=\frac{P\times T\times R}{100}=\frac{5000\times 1\times 5}{2\times 100}=₹125$
   Amount to be paid after 6 months = Principal + Interest = ₹ 5000 + 125 = ₹ 5125.
10. C.P. of agricultural land = ₹ 4,50,000
    C.P. of 13$\frac{1}{3}$ land =13×$=\frac{1}{3}\times$₹4,50,000 = ₹1,50,000
    Loss% = 15%
    S.P. of 13$\frac{1}{3}$ land =100−loss%100×C.P.$=\frac{100-loss\mathrm{\%}}{100}\times C.P.$=100−15100×1,50,000=85100×1,50,000$=\frac{100-15}{100}\times 1,50,000=\frac{85}{100}\times 1,50,000$= ₹12,750
    C.P. of 25$\frac{2}{5}$ land =25×$=\frac{2}{5}\times$ ₹. 4,50,000=₹ 1,80,000
    Gain% = 20%
    S.P. of 25$\frac{2}{5}$ land =100+Profit%100×C.P=100+20100×1,80,000$=\frac{100+Profit\mathrm{\%}}{100}\times C.P=\frac{100+20}{100}\times 1,80,000$
    Let S.P. of the remaining land = ₹ x
    Total S.P. of the land = ₹ 12,750 + ₹ 2,16,000 + ₹ x =₹ 2,28,750 + ₹ x
    Total C.P. = ₹ 4,50,000
    Overall Gain = 10%
    S.P.100+profit%100×C.P$S.P.\frac{100+profit\mathrm{\%}}{100}\times C.P$
    2,28,750+x=100+10100×4,50,000$2,28,750+x=\frac{100+10}{100}\times 4,50,000$=110100×4,50,000=4,95,000$=\frac{110}{100}\times 4,50,000=4,95,000$
    x = 4,95,000 – 2,28,750 = ₹ 2,66,250
    Therefore the S.P. of the remaining land = ₹ 2,66,250.
11. Number of people who like cricket = 60%
    Number of people who like football = 30%
    Number of people who like other games
    = 100% – (60% + 30%)
    = 100% – 90% = 10%
    Total number of people = 50 lakhs = 50,00,000
    Now number of people who like cricket
    = 60% of 50,00,000
    =60100×5000000$=\frac{60}{100}\times 5000000$
    = 30,00,000 or, 30 lakh
    Number of people who like football
    = 30% of 50,00,000
    =30100×5000000$=\frac{30}{100}\times 5000000$
    = 15,00,000 or, 15 lakh
    Number of people who like the other games
    = 10% of 50,00,000
    =10100×5000000$=\frac{10}{100}\times 5000000$
    = 5,00,000 or, 5 lakh
12. (i) P = Rs. 8000
    R = 5% per annum
    n = 2 years
    ∴A=P(1+R100)n=8000(1+5100)2$\therefore A=P{\left(1+\frac{R}{100}\right)}^n=8000{\left(1+\frac{5}{100}\right)}^2$
    =8000(1+120)2=8000(2120)2$=8000{\left(1+\frac{1}{20}\right)}^2=8000{\left(\frac{21}{20}\right)}^2$
    =8000×2120×2120=Rs.8820$=8000\times \frac{21}{20}\times \frac{21}{20}=Rs.8820$
    Hence, the amount credited against his name at the end of second year is Rs. 8820
    (ii) P = Rs. 8820
    R = 5% per annum
    n = 1 year
    ∴A=P(1+R100)n=8820(1+5100)1$\therefore A=P{\left(1+\frac{R}{100}\right)}^n=8820{\left(1+\frac{5}{100}\right)}^1$
    =8820(1+120)1=8820=2120$=8820{\left(1+\frac{1}{20}\right)}^1=8820=\frac{21}{20}$
    = Rs. 9261
    ∴ Interest for the 3rd year
    C.I. = A – P
    = Rs. 9261 – Rs. 8820 = Rs. 441
    Hence, the interst for the 3rd year is Rs. 441