Simple Equations PDF

## SIMPLE EQUATIONS ### EXERCISE 4.1 1. Complete the last column of the table. | S. No. | Equation | Value | Say, whether the Equation is Satisfied. (Yes/No) | |---|---|---|---| | (i) | x+3=0 | x=3 | No | | (ii) | x+3=0 | x=0 | No | | (iii) | x+3=0 | x=-3 | Yes | | (iv) | x-7=1 | x=7 | No | | (v)...

## SIMPLE EQUATIONS ### EXERCISE 4.1 1. Complete the last column of the table. | S. No. | Equation | Value | Say, whether the Equation is Satisfied. (Yes/No) | |---|---|---|---| | (i) | x+3=0 | x=3 | No | | (ii) | x+3=0 | x=0 | No | | (iii) | x+3=0 | x=-3 | Yes | | (iv) | x-7=1 | x=7 | No | | (v) | x-7=1 | x=8 | Yes | | (vi) | 5x=25 | x=0 | No | | (vii) | 5x=25 | x=5 | Yes | | (viii) | 5x=25 | x=-5 | No | | (ix) | m/3 = 2 | m=-6 | No | | (x) | m/3 = 2 | m=0 | No | | (xi) | m/3 = 2 | m=6 | Yes | 2. Check whether the value given in the brackets is a solution to the given equation or not: - n+5=19 (n=1) - No - 7n+5=19 (n=-2) - Yes - 7n+5=19 (n=2) - Yes - 4p-3=13 (p=1) - No - 4p-3=13 (p=-4) - Yes - 4p-3=13 (p=0) - No 3. Solve the following equations by trial and error method: (i) 5p+2=17 - p=3 (ii) 3m-14=4 - m = 6 4. Write equations for the following statements: - The sum of numbers x and 4 is 9. - **x+4=9** - 2 subtracted from y is 8. - **y-2=8** - Ten times a is 70. - **10a=70** - The number b divided by 5 gives 6. - **b/5=6** - Three-fourth of t is 15. - **3t/4=15** - Seven times m plus 7 gets you 77. - **7m+7=77** - One-fourth of a number x minus 4 gives 4. - **x/4-4=4** - If you take away 6 from 6 times y, you get 60. - **6y-6=60** - If you add 3 to one-third of z, you get 30. - **z/3+3=30** 5. Write the following equations in statement forms: (i) p+4=15 - The sum of 4 and p is 15. (ii) m-7=3 - 7 less than m is 3. (iii) 2m=7 - Double of m is 7. (iv) m/5 = 3 - One-fifth of m is 3. (v) 3m/5 = 6 - Three-fifths of m is 6. (vi) 3p+4=25 - The sum of 4 and thrice of p is 25. (vii) 4p-2=18 - 2 less than four times p is 18. (viii) p+2/2=8 - Half of the sum of ( p and 2 ) is 8. ### EXERCISE 4.2 1. Give first the step you will use to separate the variable and then solve the equation - x-1=0 - Add 1 to both sides. x=1 - x+1=0 - Subtract 1 from both sides. x=-1 - x-1=5 - Add 1 to both sides. x=6 - x+6=2 - Subtract 6 from both sides. x=-4 - y-4=4 - Add 4 to both sides. y=8 - y+4=4 - Subtract 4 from both sides. y=0 - y-4=-7 - Add 4 to both sides. y=-3 - y+4=-4 - Subtract 4 from both sides. y=-8 2. Give first the step you will use to separate the variable and then solve the equation: - 3l=42 - Divide both sides by 3. l=14 - b/2=6 - Multiply both sides by 2. b=12 - z/5=7 - Multiply both sides by 5. z=35 - a/5=15 - Multiply both sides by 5. a=75 - 4x=25 - Divide both sides by 4. x=25/4 - 20t=-10 - Divide both sides by 20. t=-1/2 3. Give the steps you will use to separate the variable and then solve the equation: - 3n-2=46 - Add 2 to both sides; then divide both sides by 3. n=16 - 5m+7=17 - Subtract 7 from both sides; then divide both sides by 5. m=2 - 20p/3=40 - Multiply both sides by 3; then divide both sides by 20. p=6 - 3p/10=6 - Multiply both sides by 10; then divide both sides by 3. p=20 4. Solve the following equations: - 10p=100 - Divide both sides by 10. p=10 - 10p+10=100 - Subtract 10 from both sides; then divide both sides by 10. p=9 - p/4=5 - Multiply both sides by 4. p=20 - -p/3=5 - Multiply both sides by -3. p=-15 - 3p/4=6 - Multiply both sides by 4; then divide both sides by 3. p=8 - 3s=-9 - Divide both sides by 3. s=-3 - 2q=6 - Divide both sides by 2. q=3 - 2q-6=0 - Add 6 to both sides; then divide both sides by 2. q = 3 - 3s+12=0 - Subtract 12 from both sides; then divide both sides by 3. s=-4 - 2q+6=0 - Subtract 6 from both sides; then divide both sides by 2. q=-3 - 2q+6=17 - Subtract 6 from both sides; then divide both sides by 2. q = 5.5 - 3s=0 - Divide both sides by 3. s=0 ### MATHEMATICS 6. Set up an equation in the following cases: - Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. (Take m to be the number of Parmit's marbles.) - **5m+7=37** - Laxmi's father is 49 years old. He is 4 years older than three times Laxmi's age. (Take Laxmi's age to be y years.) - **3y+4=49** - The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. (Take the lowest score to be l.) - **2l+7=87** - In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be b in degrees. Remember that the sum of angles of a triangle is 180 degrees). - **2b+b+b=180** ## PERCENTAGE 1. Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case. - Gardening shears bought for ₹ 250 and sold for ₹ 325. - **Profit = ₹ 75, Profit% = 30%** - A refrigerator bought for ₹ 12,000 and sold at ₹ 13,500. - **Profit = ₹ 1500, Profit% = 12.5%** - A cupboard bought for ₹ 2,500 and sold at ₹ 3,000. - **Profit = ₹ 500, Profit% = 20%** - A skirt bought for ₹ 250 and sold at ₹ 150. - **Loss = ₹ 100, Loss% = 40%** 2. Convert each part of the ratio to percentage: - 3:1 - **300%:100%** - 2:3:5 - **20%:30%:50%** - 1:4 - **25%:100%** - 1:2:5 - **10%:20%: 50%** 3. The population of a city decreased from 25,000 to 24,500. Find the percentage decrease. - **Percentage decrease = 2%** 4. Arun bought a car for ₹ 3,50,000. The next year, the price went upto ₹ 3,70,000. What was the Percentage of price increase? - **Percentage increase = 5.71%** 5. I buy a T.V. for ₹ 10,000 and sell it at a profit of 20%. How much money do I get for it? - **You get 12,000 for the TV** 6. Juhi sells a washing machine for ₹ 13,500. She loses 20% in the bargain. What was the price at which she bought it? - **She bought the machine from 16,875** 7. Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the percentage (i) of carbon in chalk. (ii) If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick? - **(i) Percentage of carbon = 12%** - **(ii) Weight of the chalk stick = 25g** 8. Amina buys a book for ₹ 275 and sells it at a loss of 15%. How much does she sell it for? - **Amina sells the book for 233.75.** 9. Find the amount to be paid at the end of 3 years in each case: (a) Principal =₹1,200 at 12% p.a. - **Amount = ₹ 1609.60** (b) Principal =₹7,500 at 5% p.a. - **Amount = ₹ 8662.50** 10. What rate gives ₹ 280 as interest on a sum of ₹ 56,000 in 2 years? - **Rate = 0.25%** 11. If Meena gives an interest of ₹ 45 for one year at 9% rate p.a.. What is the sum she has borrowed? - **She has borrowed ₹ 500** 2. Convert the given decimal fractions to per cents. (a) 0.65 - **65%** (b) 2.1 - **210%** (c) 0.02 - **2%** (d) 12.35 -**1235%** 3. Estimate what part of the figures is coloured and hence find the per cent which is coloured. - (i) 1/4 is colored, hence the percentage is **25%** - (ii) 1/2 is colored, hence the percentage is **50%** - (iii) 3/6 is colored, hence the percentage is **50%** 4. Find: (a) 15% of 250 - **37.5** (b) 1% of 1 hour - **36 seconds** (c) 20% of ₹ 2500 - **₹ 500** (d) 75% of 1 kg - **0.75 kg** 5. Find the whole quantity if (a) 5% of it is 600 - **12000** (b) 12% of it is ₹ 1080 - **₹ 9000** (c) 40% of it is 500 km - **1250 km** (d) 70% of it is 14 minutes - **20 minutes** (e) 8% of it is 40 litres - **500 litres** 6. Convert given per cents to decimal fractions and also to fractions in simplest forms: (a) 25% - **0.25, 1/4** (b) 150% - **1.5, 3/2** (c) 20% - **0.2, 1/5** (d) 5% - **0.05, 1/20** 7. In a city, 30% are females, 40% are males and remaining are children. What per cent are children? - **30% are children** 8. Out of 15,000 voters in a constituency, 60% voted. Find the percentage of voters who did not vote. Can you now find how many actually did not vote? - **40% did not vote, 6000 voters did not vote** 9. Meeta saves ₹ 4000 from her salary. If this is 10% of her salary. What is her salary? - **Meeta's salary is 40,000** 10. A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win? - **The team won 5 matches**