1. Problem 14: A contractor has 560 workers to complete a stadium part in 9 months but now must finish in 5 months. Find extra workers needed. 2. Use the work formula: Work = Number of workers \times Time. 3. Original work: $560 \times 9 = 5040$ worker-months. 4. New time: 5 months, so workers needed: $\frac{5040}{5} = 1008$. 5. Extra workers: $1008 - 560 = 448$. 6. Problem 15: Geeta types 108 words in 6 minutes. Find words typed in 30 minutes. 7. Words per minute: $\frac{108}{6} = 18$. 8. Words in 30 minutes: $18 \times 30 = 540$. 9. Problem 16: $l$ varies directly as $m$. 10. i) Equation: $l = km$. 11. ii) Given $l=6$, $m=18$, find $k$: $6 = k \times 18 \Rightarrow k = \frac{6}{18} = \frac{1}{3}$. 12. iii) Find $l$ when $m=33$: $l = \frac{1}{3} \times 33 = 11$. 13. Problem 17: Deposit 2000 earns 500 interest in 3 years. Find interest on 36000 in 3 years at same rate. 14. Simple interest formula: $I = PRT$. 15. Rate $R = \frac{I}{PT} = \frac{500}{2000 \times 3} = \frac{500}{6000} = \frac{1}{12}$. 16. Interest on 36000: $I = 36000 \times \frac{1}{12} \times 3 = 9000$. 17. Problem 18: Mass varies directly with length. 18. Given: length 16 cm, mass 192 g. 19. Relation: $m = kl$. 20. Find $k$: $192 = k \times 16 \Rightarrow k = 12$. 21. Find length for mass 105 g: $105 = 12 \times l \Rightarrow l = \frac{105}{12} = 8.75$ cm. 22. Problem 19: Naresh walks 250 steps for 200 m. Find distance for 350 steps. 23. Distance per step: $\frac{200}{250} = 0.8$ m. 24. Distance for 350 steps: $0.8 \times 350 = 280$ m. 25. Problem 20: Car travels 225 km in 25 litres. Find litres for 540 km. 26. Fuel efficiency: $\frac{225}{25} = 9$ km/litre. 27. Litres for 540 km: $\frac{540}{9} = 60$ litres. 28. Problem 21: $a$ and $b$ vary inversely: $a \times b = k$. 29. i) Table 1: - For $a=2$, $b=x$: $2 \times x = k$. - For $a=6$, $b=15$: $6 \times 15 = 90 = k$. - So $k=90$. - Find $x$: $2x=90 \Rightarrow x=45$. - Find $y$ when $b=12.5$: $y \times 12.5=90 \Rightarrow y=\frac{90}{12.5}=7.2$. - Find $z$ when $a=10$: $10 \times z=90 \Rightarrow z=9$. 30. ii) Table 2: - For $a=6$, $b=18$: $6 \times 18=108=k$. - For $a=8$, $b=P$: $8P=108 \Rightarrow P=13.5$. - For $a=Q$, $b=39$: $Q \times 39=108 \Rightarrow Q=\frac{108}{39} \approx 2.77$. - For $a=25$, $b=r$: $25r=108 \Rightarrow r=4.32$. 31. Problem 22: Cloth cost Rs 337.50 for 25 m. 32. i) Cost per meter: $\frac{337.5}{25} = 13.5$. 33. Cost for 40 m: $13.5 \times 40 = 540$. 34. ii) Length for Rs 675: $\frac{675}{13.5} = 50$ m. Final answers: 14) Extra workers = 448 15) Words in 30 min = 540 16) i) $l=km$, ii) $k=\frac{1}{3}$, iii) $l=11$ 17) Interest = 9000 18) Length = 8.75 cm 19) Distance = 280 m 20) Petrol = 60 litres 21) i) $x=45$, $y=7.2$, $z=9$; ii) $Q=2.77$, $P=13.5$, $r=4.32$ 22) i) Cost = 540, ii) Length = 50