问题1. 5支笔和6支铅笔合计₹9，3支笔和2支铅笔合₹5。找到1笔和1支铅笔的成本。
解决方案：
Let the cost of 1 pen be Rs. x
and the cost of 1 pencil be Rs. y
Now, 5 pens and 6 pencils cost Rs. 9
=> 5x + 6y = 9 (1)
And, 3 pens and 2 pencils cost Rs. 5
=> 3x + 2y = 5 (2)
Multiplying (1) by 1 and (2) by 3 and subtracting them we get:
5x+6y-9x-6y = 9-15
=> -4x = 6
=> x = 3/2
Putting x = 3/2 in equation (1), we get:
6y = 9-15/2
=> 6y = 3/2
=> y = 1/4
So, the cost of one pen is Rs. 3/2 and cost of one pencil is Rs. 1/4
问题2。7个盒式录音带和3个盒式录像带的价格为₹1110，而5个盒式录音带和4个盒式录像带的价格为₹1350。找到一个盒式录音带和一个盒式录像带的成本。
解决方案：
Let the cost of 1 audio cassette be Rs. x
and cost of 1 video cassette be Rs. y
Now, cost of 7 audio cassette and 3 video cassette is Rs. 1100
=> 7x + 3y= 1110 (1)
And, cost of 5 audio cassette and 4 video cassette is Rs. 1350
=> 5x + 4y = 1350 (2)
Multiplying (1) by 4 and (2) by 3 and subtracting them we get:
28x+12y-15x-12y = 4440-4050
=> 13x = 390
=> x = 390/13 = 30
Putting x=30 in equation (1), we get:
210+3y = 1110
=> 3y = 900
=> y = 900/3 =300
So, the cost of one audio cassette is Rs. 30 and cost of one video cassette is Rs. 300
问题3。里纳(Reena)有钢笔和铅笔，总数为40。如果她多了5支铅笔，少了5支笔，那么铅笔数将变成笔数的4倍。查找笔和铅笔的原始数量。
解决方案：
Let the number of pens be x
and the number of pencils be y
x + y = 40 (1)
Now, if she has 5 more pencils and 5 less pens, then number of pencils would become 4 times the number of pens
number of pens now = x – 5
and number of pencils now = y + 5
(y + 5) = 4 (x – 5)
=> y + 5 = 4x – 20
=> 4x – y = 25 (2)
Adding (1) and (2), we get:
5x = 65
=> x = 13
Putting x=3 in equation (1), we get:
13 + y = 40
=> y = 40 – 13 = 27
So, original number of pens were 13 and pencils were 27
问题4。4桌和3椅子的总和为1,250卢比，3桌和4椅子的价格为1950卢比。找到2桌和1桌子的成本。
解决方案：
Let the cost of 1 table be Rs. x
and the cost of 1 chair be Rs. y
Now, 4 tables and 3 chairs together cost Rs 2250
4x + 3y = 2250 (1)
And, 3 tables and 4 chairs cost Rs. 1950
3x + 4y= 1950 (2)
Multiplying (1) by 3 and (2) by 4 and subtracting them, we get:
12x+9y-12x-16y = 6750-7800
=> -7y = -1050
=> y = 1050/7 = 150
Putting y = 150 in equation (1), we get:
4x + 450 = 2250
=> 4x = 1800
=> x = 1800/4 = 450
So, the cost of 1 table and 2 chairs will be:
450 + 2(150) = Rs. 750
问题5：3袋和4支笔合计为257卢比，而4袋和3支笔合计为324卢比。找到1袋和10支笔的总成本。
解决方案：
Let the cost of 1 bag be Rs. x
and the cost of 1 pen be Rs. y
Now, 3 bags and 4 pens together cost Rs 257
3x + 4y = 257 (1)
And, 4 bags and 3 pens together cost Rs. 324
4x + 3y = 324 (2)
Multiplying (1) by 3 and (2) by 4 and subtracting them, we get:
9x+12y-16x-12y = 771-1296
=> -7x = -525
=> x = 525/7 = 75
Putting x = 75 in equation (1), we get:
225 + 4y = 257
=> 4y = 32
=> y = 32/4 = 8
So, the cost of 1 bag and 10 pens will be:
75 + 10(8) = Rs. 155
问题6：5本书和7支钢笔合计为₹79，而7本书和5支钢笔合计为₹77。找到1本书和2支钢笔的成本。
解决方案：
Let the cost of 1 book be Rs. x
and the cost of 1 pen be Rs. y
Now, 5 books and 7 pens together cost Rs. 79
5x + 7y = 79 (1)
And, 7 books and 5 pens together cost Rs. 77
7x + 5y = 77 (2)
Multiplying (1) by 7 and (2) by 5 and subtracting them, we get:
35x+49y-35x-25y = 553-385
=> 24y = 168
=> y = 168/24 = 7
Putting y=7 in equation (2), we get:
7x + 35 = 77
=> 7x = 42
=> x = 42/7 = 6
So, the cost of 1 book and 2 pens will be:
6 + 2(7) = Rs. 20
问题7. Jamila以1050卢比的价格出售了一张桌子和一把椅子，从而在桌子上赚了10％，在椅子上赚了25％。如果她在桌子上赢了25％，在椅子上赢了10％，她将得到1065卢比。找到每张的成本价。
解决方案：
Let the cost price of the table be Rs. x
and the cost price of the chair be Rs. y
The selling price of the table, when it is sold at a profit of 10% will be Rs. [x+(10/100)x]
The selling price of the chair, when it is sold at a profit of 25% will be Rs. [y+(25/100)y]
Their sum total is Rs. 1050
=> [x+(10/100)x] + [y+(25/100)y] = 1050 (1)
Had she taken 25% profit on table, selling price of it would be Rs. [x+(25/100)x]
Had she taken 10% profit on chair, selling price of it would be Rs. [y+(10/100)y]
And their sum total would be Rs. 1065
=> [x+(25/100)x] + [y+(10/100)y] = 1065 (2)
Simplifying equation (1) and (2) we get:
110x + 125y = 105000 (3)
125x + 110y = 106500 (4)
Multiplying equation (3) by 25 and equation (4) by 22 and subtracting them, we get:
2750x + 3125y – 2750x – 2420y = 2625000-2343000
=> 705y = 282000
=> y = 282000/705 = 400
Putting y = 400 in equation (3), we get:
110x + 50000 = 105000
=> 110x = 55000
=> x = 55000/110 = 500
So, the cost price table is Rs. 500 and chair is Rs. 400
问题8. Susan在A和B两个方案中投入了一定的资金，这两个方案的年利率分别为8％和9％。她获得了￥ 1860的年利息。但是，如果她将这两个计划的投资额互换，她将获得每年20卢比的利息。她在每个计划中投资了多少钱?
解决方案：
Let the amount of investments in schemes A and B be Rs. x and Rs. y, respectively.
Now she has received Rs. 1860 in total
Interest on Rs. x at the rate of 8% per annum on scheme A + Interest on Rs. y at the rate of 9% per annum on scheme B = Total amount received
=> (x*8*1)/100 + (y*9*1)/100 = 1860 [because simple interest = (principal*rate*time)/100]
=> 8x+9y = 186000 (1)
Now, if she has interchanged the investment amount, her profit would be 720 more
=> she has invested Rs. x in Scheme B and Rs. y in Scheme A
Interest on Rs. x at the rate of 9% per annum on scheme A + Interest on Rs. y at the rate of 8% per annum on scheme B = Total amount received
=> (x*9*1)/100 + (y*8*1)/100 = 1860+20
=> 9x+8y = 188000 (2)
Multiplying equation (1) by 9 and equation (2) by 8 and subtracting them, we get:
72x+81y-72x-64y = 1000(1674-1504)
=> 17y = 1000(170)
=> y = 10000
Putting y = Rs. 10000 in equation (1), we get:
8x + 90000 = 186000
=> 8x = 96000
=> x = 12000
So, she invested Rs. 12000 in Scheme A and Rs.10000 in Scheme B
问题9.板球队的教练以3800卢比的价格购买了7球拍和6球。后来，他以1750卢比的价格购买了3球拍和5球。计算每个球拍和每个球的成本。
解决方案：
Let the cost of 1 bat be Rs. x
and the cost of 1 ball be Rs. y
Now, 7 bats and 6 balls costs Rs. 3800
7x + 6y = 3800 (1)
Also, 3 bats and 5 balls costs Rs. 1750
3x + 5y = 1750 (2)
Multiplying (1) by 5 and (2) by 6 and subtracting them, we get:
35x + 30y – 18x – 30y = 19000-10500
=> 17x = 8500
=> x = 8500/17 = 500
Putting x = Rs. 500 in equation (2), we get:
1500 + 5y = 1750
=> 5y = 250
=> y = 50
So, the cost of a bat is Rs. 500 and the cost of a ball is Rs. 50
问题10.借书图书馆在前三天收取固定费用，其后每天收取一笔额外费用。莎莉莎为一本保存了七天的书支付了27卢比，而苏西为她一本保存了五天的书支付了21卢比。查找固定费用和每一天的费用。
解决方案：
Let the fixed charge for the book be Rs. x
and let the extra charge for each day be Rs. y
For seven days charge is Rs. 27, extra charge will be applicable after 3 days (for 4 days)
x + 4y = 27 (1)
For five days charge is Rs. 21, extra charge will be applicable after 3 days (for 2 days)
x + 2y = 21 (2)
Subtracting both equation, we get:
2y = 6
=> y = 3
Putting y= Rs. 3 in equation (2), we get:
x + 6 = 21
=> x = 15
So, the fixed charge amount is Rs. 15 and charges for each extra day is Rs. 3