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Question 1.Complete the table below: Sr. No Radius (r) Diameter (d) Circumference (c) i. 7 cm ii. 28 cm iii. 616 cm iv. 72.6 cm Solution:i. Radius (r) = 7 cmDiameter (d) = 2r= 2 x 7 = 14 cmCircumference (c) = πd= 22/7 x 14= 44 cm ii. Diameter (d) = 28 cm Sr. … Read more

Question 1.If the interest on Rs 1700 is Rs 340 for 2 years, the rate of interest must be__.(A) 12%(B) 15%(C) 4%(D) 10%Solution:(D) 10% Hint: Question 2.If the interest on Rs 3000 is Rs 600 at a certain rate for a certain number of years, what would the interest be on Rs 1500 under the … Read more

Question 1.If Rihanna deposits Rs 1500 in the school fund at 9 p.c.p.a for 2 years, what is the total amount she will get?Solution:Here, P = Rs 1500, R = 9 p.c.p.a , T = 2 years = 1500 x 9 x 2= Rs 270∴ Total amount = Principal + Interest= 1500 + 270= Rs … Read more

Question 3.Shweta, Piyush and Nachiket together invested Rs 80000 and started a business of selling sheets and towels from Solapur. Shweta’s share of the capital was Rs 30000 and Piyush’s Rs 12000. At the end of the year they had made a profit of 24%. What was Nachiket’s investment and what was his share of … Read more

Question 1.Five workers take 12 days to weed a field. How many days would 6 workers take? How many would 15 take?Solution:Let 6 workers take x days and 15 workers take y days to weed the field.The number of workers and the time required to weed the field are in inverse proportion.∴ 6 × x … Read more

Question 1.If 7 kg onions cost Rs 140, how much must we pay for 12 kg onions?Solution:Let the cost of 12 kg onions be Rs x.The quantity of onions and their cost are in direct proportion. = 240We must pay Rs 240 for 12 kg onions. Question 2.If Rs 600 buy 15 bunches of feed, … Read more

Question 1.Simplify (3x – 11y) – (17x + 13y) and choose the right answer.(A) 7x – 12y(B) -14x – 54y(C) -3(5x + 4y)(D) -2(7x + 12y)Solution:(D) -2(7x + 12y) Hints:(3x – 11y) – (17x + 13y) = 3x – 11y – 17x – 13y= – 14x – 24y= – 2 × 7x – 2 × … Read more

Question 1.Multiply:i. 16xy × 18xyii. 23xy² × 4yz²iii. (12a + 17b) × 4civ. (4x + 5y) × (9x + 7y)Solution:i. 16xy × 18xy= 16 × 18 × xy × xy= 288x²y² ii. 23xy² × 4yz²= 23 × 4 × xy² × yz²= 92xy³z² iii. (12a + 17b) × 4c = 12a × 4c + 17b … Read more

Question 1.Subtract the second expression from the first.i. (4xy – 9z); (3xy – 16z)ii. (5x + 4y + 7z); (x + 2y + 3z)iii. (14x² + 8xy + 3y²); (26x² – 8xy – 17y²)iv. (6x² + 7xy + 16y²); (16x² – 17xy)v. (4x + 16z); (19y – 14z + 16x)Solution:i. (4xy – 9z) – (3xy … Read more

Chapter 8 Algebraic Expressions and Operations on Them Set 8.2 Question 1.Add:i. 9p + 16q; 13p + 2qii. 2a + 6b + 8c; 16a + 13c + 18biii. 13x² – 12y²; 6x² – 8y²iv. 17a²b² + 16c; 28c – 28a²b²v. 3y² – 10y + 16; 2y – 7vi. – 3y² + 10y – 16; 7y² … Read more