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1. 34% 2. Second offer is better 3. 1.2% 1. ` 1,847 approx. 2. 5,865 workers
Chapter 11 Chapter 12
Exercise 11.1 Exercise 12.1
1. (a) ` 877.25; ` 2,527.25 (b) ` 4,917.50; ` 33,017.50 1. Constants = –73 and 49; Variables = 7a, bc , 16b and xyz
2
2
(c) ` 1,554; ` 10,804 2. ` 6,10,285 3. ` 313.90 2. (a) 3 (b) 4 (c) 1 (d) 2
4. ` 5,350 5. ` 4,800 6. ` 1,430 7. 16% p.a. 3. Monomials: 4x ÷ 5, 7x y
3 2
8. 3 years 2 months 9. 8 years 4 months Binomials: x + 3a b, x – y, 19x y × 7xy – yz ÷ 4
3
2
9 10
2
3
10. ` 16,800 gives more interest; ` 545 11. ` 625.80 Trinomials: 82 + yz – z , y – 7z y + x 4
3
3
3
12. ` 32,030 4. (a) –5 (b) 12xyz (c) y z 5. (a) 7 (b) 8y (c) xyz
2
3 2
7 2
Exercise 11.2 (d) y (e) 2a (f) –1 (g) x yz
7
1. ` 1,780.80 2. ` 278.18 3. ` 21,224.16 6. (a) Not a polynomial (b) Degree 4
4. ` 989.19 5. ` 259.20 6. ` 9,288.18 (c) Degree 7 (d) Not a polynomial
Exercise 11.3 7. (a) 2 (b) 2 (c) 8 (d) 3
2 2
2 2
2 2
1. (a) ` 764.06 (b) ` 646.52 (c) ` 4,310.13 8. 24xyz and –13yzx; 13a b , 2a b and 24b a ;
7
2. ` 10,125 3. ` 19.33 4. ` 50.00 5. ` 5,846.01 –9a b and 13 a b
3 3
3 3
6. ` 45.45 7. ` 918.12 8. ` 8 9. ` 1.22
Exercise 12.2
9
Exercise 11.4 1. (a) ab (b) –17xy (c) –1.7x 2
3
1. 3 years 2. 20% p.a. 3. ` 6,250 4. ` 7,680 2 5
2
2
2
5. ` 6,400 6. 4% p.a. 7. ` 1,261 8. 8% p.a. 2. (a) pq (b) 8ab c (c) x y
2
5
9. ` 7,806.54 10. 41.4% p.a. 3. (a) 18x + 8y + 18z (b) 7x + 4y – 12z – 10
11. 8% (c) 4x – 2x (d) 2x – 3x + 7x + 8
3
2
2
3
R 2 PRT 4. (a) x + 7x – 3 (b) 3x + 10y (c) 2x + 6y + 2z
2
2
2
2
(Hint: C.I. – S.I. = P 1+ − 1 −
100 100 (d) 4x + 2xy – 2y 5. –2x – 7xy 6. 9a – 26b
3
2
2
R 2 R PR 7. 12a – 13a + 37a – 20 8. 13p – 2q
4
3
= P + − )
10,000 100 50 Exercise 12.3
12. 1½ years 13. ` 64,000 14. 12½ years 3
1. (a) –15p (b) 10 a b (c) –3x y z
6 5
5
3 6 3
Exercise 11.5 (d) 1 p q (e) 6x – 13xy – 28y 2
2
2 4
1. 5,618 (approx.) 2. 5,237 (approx.) 3. 3,50,000 10 2 2 3 3 4 2
4. 5% per year 5. 11,136 years 6. 20,000 (f) –9x y – 2xy + 5x y (g) 35x + 21x – 14
2. (a) 18x + 33xy – 30y (b) 3a x – 3aby + 3acz
2
2
1
Exercise 11.6 (c) 9x + 9x – 4 (d) x + – (e) 30x y – 20xy 2
x
2
3
2
1. (a) ` 1,44,400 (b) ` 1,37,180 2. ` 4,97,028.34 6 6
3
7
4
2
5
3
2
3. ` 7,257.60 per kg 4. 3 years 5. 20% p.a. (f) 6x – 17x + 21x – 12 (g) x + 2x – x + 2x – 2x – 2
2
2
2
2
2
2
6. ` 10,000 7. 3 years (h) a b + a c + ab + b c + bc + ac + 3abc
(i) 2x – 2xy + 5x y – 5y (j) 2x + 7x + 13x + 10x + 8
3
3
2
2
2
3
4
Mental Maths (k) x + 7x – 6x – 72 (l) 12x – 23x + 31x – 14
2
3
2
3
1. (a) (ii) (b) (iii) (c) (ii) (d) (iv) (e) (i) 3. (a) b 2 (b) –2y 2 (c) 3d 5 (d) –1– 3 + 2b
2 4
2. (a) Compounding, simple (b) relative (c) usage, wear 2a 2 x z 10x ab 2 a
1
1
2 2
(d) ` 1,463.42 (e) l n + 4n + 2lm (f) 6 – 3pq r – 2p q r
2 4 2
3 2
16
2
2
Practice Time 4. (a) 3x + 1 (b) 4x – 5 (c) x – 2 (d) x + 4
3
2
2 2
4
4
3
2
1. ` 2,388.30 2. ` 218 3. ` 310 4. 12.5% p.a. (e) a(a – b ) (f) x + x y + x y + xy + y (g) x – 3x + 2
5. Kusum; 4,320 6. ` 5,000 7. 1 year 8. 1½ years 5. (a) –x – y (b) –x + y – z (c) 42ab – 12a 2
9. ` 1,000, 10% p.a. 10. ` 8,000, 10% p.a. 11. ` 5,000 (d) 19p – 25q
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