第10章正向和反向变化–练习10.1 |套装1
问题11：一辆汽车以50 km / hr的平均速度行驶。它会在12分钟内移动多少距离。
解决方案：
Distance covered by the car in 1 hour = 50 km
Therefore, the distance covered by car in 60 minutes = 50 km (1 h = 60 min)
Now,
Distance covered by the car in 1 minute = 50/60 (Taking 60 to RHS)
Distance covered by the car in 12 minutes = Distance covered by the car in 1 minutes x Required minutes
=>Distance covered by the car in 12 minutes = (50/60) x 12
Solving the above equation, we get
=> Distance covered by the car in 12 minutes = 10 km
问题12. 68箱某种商品需要的货架长度为13.6 m。多少盒相同的商品将占据20.4 m的货架?
解决方案：
Given,
Let the number of boxes required for length 20.4m be x.
| Boxes | 68 | x |
| Shelf length (in m) | 13.6 | 20.4 |
We have the following equation,
=> 68/13.6 = x/20.4
Solving for x,
x = (68 / 13.6) x 20.4
x = 102 boxes
Therefore, 102 boxes are required to cover a shelf of 20.4m
问题13.在图书馆中，一本书的136册需要3.4米的书架长。同一本书的多少副本将占据5.1米的书架长度?
解决方案：
Given,
Let the number of required shelves be x.
| Copies | 136 | x |
| Shelf length(in m) | 3.4 | 5.1 |
We have the following equation,
=> 136/3.4 = x/5.1
Solving for x,
x = (136 / 3.4) x 5.1
x = 204 books
Therefore, 204 books are required to cover a shelf of 5.1 m
问题14：240公里路程的二等铁路票价为卢比。 15.00。 139.2公里的路程票价是多少?
解决方案：
Railway fare for 240 km = Rs 15.00
Let the railway fare for 139.2 km be x.
| Distance (in km) | 240 | 139.2 |
| Price (in Rs) | Rs 15 | x |
We have the following equation,
=> 240 / 139.2 = 15 /x
Solving for x, we get ,
=> x = 5 x 139.2 / 240
=> x = Rs 87
Therefore, railway fare for a journey of 139.2 km = Rs 87.
问题15.如果一堆12纸板的厚度为35毫米，则求出294纸板的厚度。
解决方案：
Thickness of 12 cardboards = 35 mm
Thickness of 1 cardboard = 35/12 mm
| Cardboards | 12 | 294 |
| Thickness (in mm) | 35 | x |
Thickness of 294 cardboards = Thickness of 1 cardboard x 294
=> Thickness of 294 cardboards = (35/12) x 294
=> Thickness of 294 cardboards = 85.75 mm
问题16. 97米布的成本为Rs。 242.50。可以购买多长的卢比。 302.50?
解决方案：
Length of cloth in Rs 242.50 = 97 m
Length of cloth in Rs 302.50 = x
| Cloth length(in m) | 97 | x |
| Price | 242.50 | 302.50 |
Solving for x, we get ,
=> 97/x = 242.50/302.50
=> 97/x = 24250/30250
=> x = (97 × 30250)/24250
=> x = 121 m
问题17：11个人可以在一天之内挖出6 3/4米长的海沟。一天要雇多少人来挖27米长的相同类型的?沟?
解决方案：
| Men | 11 | x |
| Length of trench (in m) | 6+ 3/4 = 27/4 | 27 |
11 / (27/4) = x/27
Solving for x, we get,
(11 × 27)/(27/4) = x
Cancelling the numerator and denominator, we get,
x = (11 × 4) men
x = 44 men
Therefore,
44men can dig 27m long trench in one day
问题18：工人的收入为卢比。 210天，共工作6天。如果他本月的总收入为卢比。 875，他工作了多少天?
解决方案：
Days for which Rs 210 paid to worker = 6
Days for which Rs 875 paid to worker = x
| Days | 6 | x |
| Salary | 210 | 875 |
Equating , we have,
210/6 = 875/x
Solving for x, we have,
x = (875 × 6)/210
x= 25 days
问题19.工人的工资为卢比。 200工作8天。如果他工作20天，他会得到多少?
解决方案：
Salary for 8 days of work = Rs 200
Salary for 20 days of work = x
| Salary | 200 | x |
| Days | 8 | 20 |
Solving for x, we have,
8 /200 = 20/x
=> x =( 20 × 200) /8
=> x = (20 × 25)
=> x= Rs 500
Therefore, Salary for 20 days of work = Rs 500
问题20.一根弹性字符串的延伸量随其上的重量而直接变化。如果150 gm的重量产生2.9厘米的延伸量，那么什么重量会产生17.4厘米的延伸量?
解决方案：
Weight required to produce extension of 2.9 cm = 150 gm
Weight required to produce extension of 17.4 cm = x
| Extension (in cm) | 2.9 | 17.4 |
| weight (in gm) | 150 | x |
Solving for x, we have,
150 /2.9 = x/17.4
(150 /2.9) × 17.4 = x
=> x = 900gm
Therefore, Weight required to produce extension of 17.4 cm = 900 gm
问题21.弹性弹簧中的伸展量直接随其上的重量而变化。如果250 gm的重量产生3.5厘米的延伸，请找到700 gm的重量产生的延伸。
解决方案：
Extension produced by 250gm of weight = 3.5 cm
Extension produced by 700gm of weight = x
| Extension (in cm) | 3.5 | x |
| weight (in gm) | 250 | 700 |
By the following data, we have,
250 /3.5 = 700/x
Solving for x,
(700 × 3.5) /250 = x
=> x = (7 × 35) /25
=> x = 9.8 cm
Extension produced by 700gm of weight = 9.8 cm
问题22：在十天内，地球从大气中吸收了2.6×10 8磅的灰尘。 45天内会收集多少灰尘。
解决方案：
We have,
| Dust(in pounds) | 2.6 × 108 | x |
| Days | 10 | 45 |
Pounds of dust picked up in 10 days = 2.6 × 108
Pounds of dust picked up in 45 days = x
Solving for x, we have,
10 / (2.6 × 108) = 45 /x
x = (2.6 × 108 × 45) /10
=> x = 11.7 × 108 pounds
Therefore, earth will pick up 11.7 × 108 pounds of dust in45 days.
问题23：在15天之内，地球从大气中吸收了1.2 x 108千克的灰尘。多少天后会捡起4.8 x 10s公斤的灰尘?
解决方案：
We have,
| Days | 15 | x |
| Dust | 1.2 × 108 | 4.8 × 108 |
Solving for x, we get,
1.2 × 108 /15 = 4.8 × 108 /x
x = (4.8 × 108 × 15) / (1.2 × 108)
=> x = (4.8 × 15) / 1.2
=> x = 60 days
Therefore, earth will pick up 4.8 × 108 kg of dust in 60 days.