问题11. 4支笔和4个铅笔盒的价格是100卢比。三倍于一支笔的价格比一个铅笔盒的价格高了15卢比。为上述情况形成一对线性方程式。查找笔盒的成本。
解决方案：
Let the cost of a pen be Rs. x
and the cost of a pencil box be Rs. y.
Now, the cost of 4 pens and 4 pencil boxes is Rs 100.
4x + 4y = 100
=> x + y = 25 (1)
And, three times the cost of a pen is ₹ 15 more than the cost of a pencil box
3x = y + 15
=> 3x – y = 15 (2)
On adding Equation (1) and (2), we get:
4x = 40
=> x = 10
Putting x = Rs. 10 in equation (1), we get:
10 + y = 25
=> y = 25 – 10 = 15
So, the cost of a pen and a pencil box are ₹ 10 and ₹ 15, respectively.
问题12：有人说：“给我一百个朋友！然后，我将成为你的两倍。”其他人回答说：“如果给我十分，我的财富将是你的六倍。”告诉我他们各自的资本额是多少?
解决方案：
Let the amount of first person be Rs. x
and amount of second one be Rs. y
Now, upon giving Rs. 100 to first from second, first person will have twice the amount of the second
x + 100 = 2 (y- 100)
=> x + 100 = 2y – 200
=> x – 2y = -200 – 100
=> x – 2y = -300 (1)
Also, if Rs. 10 is given to second from first, it will have six times the amount of first
6(x – 10) = (y + 10)
=> 6x – 60 = y + 10
=> 6x – y = 10 + 60
=> 6x – y = 70 (2)
Multiplying (i) by 1 and (ii) by 2 and subtracting them, we get:
x – 2y – 12x + 2y = -300-140
=> -11x = -440
=> x = 440/11 = 44
Putting x = Rs. 44 in equation (1), we get:
44 – 2y = -300
=> 340 = 2y
=> y = 170
Hence first person has money Rs. 40 and second person has Rs. 17
问题13. A和B都有一定数量的芒果。 A对B说：“如果您给您30个芒果，我剩下的将是您的两倍。” B回答：“如果给我10个，我将剩下三倍。”每个有多少个芒果?
解决方案：
Let A has x mangoes
and B has y mangoes
According to the first condition,
x + 30 = 2 (y – 30)
=> x + 30 = 2y – 60
=> x – 2y = -60 – 30
=> x – 2y = -90 (1)
and according to the second condition
3 (x – 10) = (y + 10)
=> 3x – 30 = y + 10
=> 3x – y = 10 + 30
=> 3x – y = 40 (2)
Multiplying equation (1) with 1 and equation (2) with 2 and subtracting them, we get:
x – 2y – 6x + 2y = -90 -80
=> -5x = -170
=> x = 34
Putting x = 34 in equation (1), we get:
34 – 2y = -90
=> 2y = 124
=> y = 62
So, A has 34 mangoes and B has 62 mangoes
问题14. Vijay有一些香蕉，他将它们分为A和B两部分。他以3香蕉的₹2的价格卖出了第一手，每根香蕉的₹1出售了第二手，总共得到了₹ 400.如果他以每只香蕉1卢比的价格卖出了第一手拍品，而每五个香蕉以4卢比的价格卖出了第二手拍品，那么他的总收藏额将是460卢比。找到他拥有的香蕉总数。
解决方案：
Let the number of bananas in lots A and B be x and y, respectively.
Now,
Cost of the first lot at the rate of ₹ 2 for 3 bananas + Cost of the second lot at the rate of ₹ 1 per banana = Amount received (Rs. 400)
=> (2/3) x + y = 400
=> 2x + 3y= 1200 (1)
Also,
Cost of the first lot at the rate of ₹ 1 per banana + Cost of the second lot at the rate of ₹ 4 for 5 bananas = Amount received (Rs. 460)
=> x + (4/5) y = 460
=> 5x + 4y = 2300 (2)
On multiplying in the Equation (1) by 4 and Equation (2) by 3 and subtracting them, we get:
8x + 12y -15x – 12y = 4800-6900
=> -7x = -2100
=> x = 300
Putting x = 300 in equation (1), we get:
600 + 3y = 1200
=> 3y = 600
=> y = 200
So, total numbers of bananas he had was (300+200) = 500
问题15：以5％的利润出售电视机和以10％的利润出售冰箱时，店主获得了2000卢比。但是，如果他以10％的利润出售电视而以5％的损失出售冰箱。他从交易中获得₹1500。查找电视和冰箱的实际价格。
解决方案：
Let the price of T.V. be Rs. x
and price of Fridge be Rs. y
Now, on selling a T.V. at 5% gain and a fridge at 10% gain, gain is Rs. 2000
(x*5)/100 + (y*10)/100 = 2000
=> x + 2y = 40000 (1)
Also, if he sells the T.V. at 10% gain and the fridge at 5% loss, gain is Rs. 1500
(x*10)/100 – (y*5)/100 = 1500
=> 2x – y = 30000 (2)
Multiplying equation (1) by 2 and subtracting it from equation (2), we get:
2x + 4y – 2x + y = 80000 – 30000
=> 5y = 50000
=> y = 10000
Putting y = Rs. 10000 in Equation (2), we get:
2x – 10000 = 30000
=> 2x = 40000
=> x = 20000
So, the cost of T.V. is Rs. 20000 and cost of fridge is Rs. 10000