问题1.下表x和y在以下哪个表中成反比：
一世)
|
x |
4 |
3 |
12 |
1 |
|
y |
6 |
8 |
2 |
24 |
解决方案：
In order to show x and y vary inversely,
x and y should be equal to Constant i.e x × y = Constant
So, 4 × 6 = 24
3 × 8 = 24
12 × 2 = 24
1 × 24 = 24
Since the product of xy in all cases is 24 (i.e Constant)
Hence, in this question, x and y vary inversely
ii)
|
x |
5 |
20 |
10 |
4 |
|
y |
20 |
5 |
10 |
25 |
解决方案：
In order to show x and y vary inversely,
x and y should be equal to Constant i.e x × y = Constant
So, 5 × 20 = 100
20 × 5 = 100
10 × 10 = 100
4 × 25 = 100
Since the product of xy in all cases is 100 (i.e Constant)
Hence, in this question, x and y vary inversely
iii)
|
x |
4 |
3 |
6 |
1 |
|
y |
9 |
12 |
8 |
36 |
解决方案：
In order to show x and y vary inversely,
x and y should be equal to Constant i.e x × y = Constant
So, 4 × 9 = 36
3 × 12 = 36
6 × 8 = 48
1 × 36 = 36
Since the product of xy in all cases is not Constant.
Hence, in this question, x and y don’t vary inversely
iv)
|
x |
9 |
24 |
15 |
3 |
|
y |
8 |
3 |
4 |
25 |
解决方案：
In order to show x and y vary inversely,
x and y should be equal to Constant i.e x × y = Constant
So, 9 × 8 = 72
24 × 3 = 72
15 × 4 = 60
3 × 25 = 75
Since the product of xy in all cases is not Constant.
Hence, in this question, x and y don’t vary inversely
问题2. x和y成反比，请填写以下空白：
一世)
|
x |
12 |
16 |
….. |
8 |
….. |
|
y |
….. |
6 |
4 |
…… |
0.25 |
解决方案：
Since it is given that x and y vary inversely,
So, x × y = Constant
|
x |
12 |
16 |
b |
8 |
d |
|
y |
a |
6 |
4 |
c |
0.25 |
Finding the value of ‘a’
12 × a = 16 × 6
=> a = 8
Finding the value of ‘b’
16 × 6 = b × 4
=> b = 24
Finding the value of ‘c’
24 × 4= 8 × c
=> c = 12
Finding the value of ‘d’
8 × 12 = d × 0.25
=> d = 384
Hence, the values of a, b, c, and d are 8, 24, 12, and 384.
ii)
|
x |
16 |
32 |
8 |
128 |
|
y |
4 |
….. |
….. |
0.25 |
解决方案：
Since it is given that x and y vary inversely,
So, x × y = Constant
|
x |
16 |
32 |
8 |
128 |
|
y |
4 |
a |
b |
0.25 |
Finding the value of ‘a’
16 × 4 = 32 × a
=> a = 2
Finding the value of ‘b’
32 × 2 = 8 × b
=> b = 8
Hence, the values of a and b are 2 and 8.
iii)
|
x |
9 |
….. |
81 |
243 |
|
y |
27 |
9 |
….. |
1 |
解决方案：
Since it is given that x and y vary inversely,
So, x × y = Constant
|
x |
9 |
a |
81 |
243 |
|
y |
27 |
9 |
b |
1 |
Finding the value of ‘a’
9 × 27 = a × 9
=> a = 27
Finding the value of ‘b’
27 × 9 = 81 × b
=> b = 3
Hence, the values of a and b are 27 and 3.
问题3.以下哪个数量彼此成反比?
(i)雇用x人修建隔离墙的人数以及y完成工作所花费的时间。
(ii)乘车旅行的长度x和机票的价格y。
(iii)汽车行驶的行程(x公里)和所消耗的汽油(y升)。
解决方案：
i) If more men will be hired then the time taken will be less and if fewer men will be hired, the time taken to finish work will be more. So, here x and y vary inversely.
ii) If the length of the journey is more than the price of the ticket will also be more and vice-versa. So, here x and y vary directly.
iii) If the length of the journey is more than the consumption of petrol will also be more and vice-versa. So, here x and y vary directly.
问题4众所周知，对于给定的气体质量，体积v与压力p成反比。填写下表中缺少的条目：
|
x |
….. |
48 |
60 |
….. |
100 |
…… |
200 |
|
y |
2 |
….. |
3/2 |
1 |
…… |
1/2 |
…… |
解决方案：
Since it is given that volume ‘v’ and pressure ‘p’ vary inversely,
So, v × p = Constant
|
x |
a |
48 |
60 |
c |
100 |
e |
200 |
|
y |
2 |
b |
3/2 |
1 |
d |
1/2 |
f |
Finding the value of ‘a’
a × 2 = 60 × 3/2
=> a = 45
Finding the value of ‘b’
48 × b = 60 × 3/2
=> b = 15/8
Finding the value of ‘c’
60 × 3/2 = c × 1
=> c = 90
Finding the value of ‘d’
90 × 1 = 100 × d
=> d = 0.9
Finding the value of ‘e’
100 × 0.9 = e × 1/2
=> e = 180
Finding the value of ‘f’
180 × 1/2 = 200 × f
=> f = 9/20
Hence, the values of a, b, c, d, e and f are 45, 15/8, 90, 0.9, 180 and 9/20.
问题5.如果36个人可以在25天内完成一件工作，那么15个人将在几天内完成工作?
解决方案：
As we know if the number of men will increase, they will take fewer days. So, the number of men and days vary inversely. Let 15 men can finish the work in a days
|
Number of Men |
36 |
15 |
|
Days to finish work |
25 |
a |
So, 36 × 25 = 15 × a
=> a = 60 days
Hence, 15 men can finish the work in 60 days
问题6.由50名工人和承包商组成的劳动力可以在5个月内完成一件工作。 125个人可以在多少个月内完成相同的工作?
解决方案：
As we know if the number of men will increase, they can finish the work in fewer months. So, the number of men and months vary inversely. Let 125 men can finish the work in a months
|
Number of Men |
50 |
125 |
|
Months to finish work |
5 |
a |
So, 50 × 5 = 125 × a
=> a = 2 months
Hence, 125 men can finish the work in 2 months
问题7.一支由420名工人与承包商组成的劳动力可以在9个月内完成某项工作。在7个月内，他必须雇用多少额外的人来完成工作?
解决方案：
As we know if the number of men will increase, they can finish the work in fewer months. So, the number of men and months vary inversely. Let a man can finish the work in 7 months
|
Number of Men |
420 |
a |
|
Months to finish work |
9 |
7 |
So, 420 × 9 = a × 7
=> a = 540 men
Total men = 540
Number of men already working = 420
So, number of extra men = 540 – 420 = 120 men
Hence, 120 extra men can finish work in 7 months.
问题8：1200名男子可以在35天内吃完一顿食物。多少人应该加入他们的行列，以使同一批存货可持续使用25天?
解决方案：
As we know if the number of men will increase, they can finish the stock of food in fewer days. So, the number of men and the stock of food vary inversely. Let a man can finish the stock of food in 25 days
|
Number of Men |
1200 |
a |
|
Days to finish stock of food |
35 |
25 |
So, 1200 × 35 = a × 25
=> a = 1680 men
Total men = 1680
Number of men already present = 1200
So, number of more men required = 1680 – 1200 = 480 men
Hence, 480 more men should join to finish the stock of food within 25 days.
问题9：在一个有50名女孩的旅馆中，有40天的食物供应。如果再有30个女孩加入旅馆，这些规定将持续多久?
解决方案：
As we know if the number of girls will increase, they can finish the food provisions in fewer days. So, the number of girls and food provisions vary inversely. Let the food provisions will end in a days
|
Number of Girls |
50 |
80 |
|
Days to finish food provision |
40 |
a |
So, 50 × 40 = 80 × a
=> a = 25 days
Hence, if 30 more girls join the hostel the food provision will end in 25 days