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Math answer :
A. 100000 TK.
B. 40%
C. 3000 TK.
Full Math Solution:
1. Mr Karim gave 40% of the money he had ,to his wife . He also gave 20% of the remaining amount to each of his three sons. Half of the amount now left was spent on miscellaneous items and the remaining amount of Tk. 12,000 was deposited in the bank. How much money did Mr. Karim have initially ?
Explanation :
Let the initial amount with Mr. Karim be Tk. x
Then Money given to wife = Tk. 40100x
= Tk. 2x5 Balance = Tk. (x−2x5) = Tk. 2x5
Money given to 3 sons = Tk. [3×(20100×3x5)]
= Tk. 9x25
Balance = Tk.(3x5−9x25)
= Tk. .6x25
Amount deposited in bank = Tk. (12×6x25)
= Tk. 3x25
3x25 = 12000 ⇔ x=(12000×253)
= 100000
So, Mr Karim initially had Tk. 1,00,000 with him
Short-cut Method : Let the initial amount with Mr. Karim be Tk. x
Then ,12[100−(3×20)]
% of (100 – 40)% of x
= 12000
⇔ 12×40100×60100×x
= 12000 ⇔325x = 12000 ⇔ x=(12000×253) = 100000
Ans: Tk. 100000
2. A dealer buys dry fruits at the rate of Tk. 100, Tk. 80 and Tk. 60 per kg. He bought them in the ratio Tk. 12 : 15 : 20 by weight. He in total gets 20% profit by selling the first two and at last he finds he has no gain no loss in selling the whole quantity which he had. What was the percentage loss he suffered for the third quantity?
Solution:
Total cost of first two variety = Tk (100×12 + 80×15) = Tk 2400.
Total gain from selling frist two variety = Tk 2400×20% = Tk 480.
So, by selling 20 kg of the third variety of fruit, the dealer suffered a loss of Tk 480.
So, loss per kg of third variety of fruit = Tk. 480 ÷ 20 = Tk 24.
Loss percentage = (24/60 × 100)% = 40%
Answer: 40%
Alternative solution:
Suppose, the dealer suffered a loss of Tk x by selling a kg of the third variety of fruit.
According to the question,
20x = 0.2(100×12 + 80×15)
or, 20x = 480
or, x = 24.
So, the loss percentage = (24×100/60)% = 40%
Shortcut: Solution:
3. In a business A invests 600 more than B. The capital of B remained invested for 7 1/2 months, while the capital of A remained invested for 2 months. If the total profit be Tk. 620 and B gets Tk. 140 less than A gets then what is the amount of A’s Capital?
Solution:
Suppose, the amount of A’s capital is = Tk x
So, the amount of B’s capital is = Tk (x-600)
B’s capital remained invested for 7.5 months.
A’s capital remained invested for (7.5+2) = 9.5 months.
Suppose, total duration of the business is n months.
Suppose,
Out of Tk 620/- profit, B gets = Tk y
So, A gets = Tk (y+140)
So,
y+140+y = 620
or, y = 240
B gets = Tk 240/-
A gets = Tk 240+140 = Tk 380/-
According to the question,
9.5x/n : 7.5(x-600)/n = 380 : 240
19x : 15(x-600) = 19 : 12
15x – 9000 = 12x
3x = 9000
x = 3000
Answer: 3000 TK.
