Janata AEO (RC) --- Written Maths
22-09-2017
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Solved by : Sultan Mahmud
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7) In a class of 40 students, each student plays at least one of the games: chess, carom and table tennis. Among the students, 18 play chess, 20 play table tennins and 27 play carom. Further, 7 students play both chess and table tennis, 12 play both table tennis and carom and 4 play chess, carom and table tennis together. Find the number of students who play chess and carom but not table tennis.
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Solution:
Here,
n(total) = 40
n(chess) = 18, n(TT) = 20, n(carom) = 27.
n(chess & TT) = 7, n(TT & carom) = 12.
n(chess & TT & carom) = 4
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We have:
n(total) = n(chess) + n(TT) + n(carom) - n(chess & TT) - n(TT & carom) - n(chess & carom) + n(chess & TT & carom)
40 = 18+20+27 -7 - 12 - n(chess & carom) + 4
n(chess & carom) = 10
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So, total number of students who play both chess & carom is = 10.
But there are 4 students who play all the three games.
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So, the number of students who play chess and carom but not table tennis is = 10-4 = 6.
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Ans: 6
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8) Aslam and Babul invested in a business in the ratio 3:2. Assume that 5 percent of total profit goes to workers' provident fund. If Aslam's share is Tk. 855000, what is the amount of total profit?
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Solution:
According to the question, 5% of total profit goes to WPF.
So, the remaining 95% of profit is distributed between Aslam and Babul.
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Suppose,
Aslam's profit share is = 3x
So, Babul's profit share is = 2x
So, total profit after WPF deduction (i.e: 95% of total profit) = 3x+2x = 5x
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According to the question:
3x = 855000
5x = 855000×5/3 = 1425000
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So, 95% of total profit = 1425000
100% of total profit = 1425000×100/95 = 1500000
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Ans: Tk. 1500000
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9) Alam invested an amount of Tk. 13900 divided in two different deposits at Bank X and Bank Y at the simple interest rate of 14 percent and 11 percent per annum, respectively. If the total amount of simple interest earned in two years is Tk. 3058, what was the amount invested in the deposit of Bank Y?
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Solution:
Suppose, the amount invested in Bank Y was = Tk. p
So, the amount invested in Bank X was = Tk. (13900-p)
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According to the question:
2{14(13900-p)/100 + 11p/100} = 3058
(194600 - 14p + 11p)/100 = 1529
p = 13900
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Ans: Tk. 13900.
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10) Rashed is driving at a speed of 120 km per hour. Mahi started one hour late and started driving at a speed of 140 km per hour. How long will it take for Mahi to catch up Rashed?
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Solution:
When Mahi starts, Rashed is 120×1 = 120 km away from her.
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Relative speed of Mahi over Rashed = 140-120 kmph = 20 kmph.
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Required time to catch up Rashed = 120/20 hr = 6 hr.
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Ans: 6 hours.
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11) A table is three times as long as it is wide. If it were 5 feet shorter and 5 feet wider, it would be a square. How long and how wide is the table?
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Solution:
Let, the width of the table is x feet.
So, the length of the table is 3x feet.
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According to the question:
3x-5 = x+5
2x = 10
x = 5
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So, the length of the table is = 3×5 = 15 feet,
and the width of the table is = 5 feet.
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Ans: 15 feet, 5 feet.
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12) Given a = 3 + 2√2, find the value of (√a - 1/√a)
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Solution:
given, a = 3 + 2√2
or, a = 2 + 1 + 2√2 = (√2)² + 2×√2×1 + 1² = (√2 + 1)²
so, √a = (√2+1)
so, 1/√a = 1/(√2+1) = (√2-1)/{(√2+1)(√2-1)} = (√2-1)
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Therefore, √a - 1/√a = (√2+1) - (√2-1) = 2.
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Ans: 2.
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13) In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is Tk. 5600. The cost of 9 shirts, 9 pairs of trousers and 6 hats is Tk. 12900. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?
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Solution:
Suppose, the cost of a shirt is x, a pair of trousers is y and a hat is z.
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According to the question:
4x+4y+2z = 5600 -------------- (i)
9x+9y+6z = 12900 --------------- (ii)
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(i) × 2.25 => 9x+9y+4.5z = 12600 ------------ (iii)
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Subtracting (iii) from (ii) we get:
1.5z = 300
z = 200.
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Substituting hte value of z in (i) we get:
4x+4y + 2×200 = 5600
4x+4y = 5200
x+y = 1300
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So, x+y+z = 1300+200 = 1500.
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So, total cost of 1 shirt, 1 pair of trousers and 1 hat is Tk. 1500.
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Ans: Tk. 1500.
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22-09-2017
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Solved by : Sultan Mahmud
----
----
:
7) In a class of 40 students, each student plays at least one of the games: chess, carom and table tennis. Among the students, 18 play chess, 20 play table tennins and 27 play carom. Further, 7 students play both chess and table tennis, 12 play both table tennis and carom and 4 play chess, carom and table tennis together. Find the number of students who play chess and carom but not table tennis.
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Solution:
Here,
n(total) = 40
n(chess) = 18, n(TT) = 20, n(carom) = 27.
n(chess & TT) = 7, n(TT & carom) = 12.
n(chess & TT & carom) = 4
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We have:
n(total) = n(chess) + n(TT) + n(carom) - n(chess & TT) - n(TT & carom) - n(chess & carom) + n(chess & TT & carom)
40 = 18+20+27 -7 - 12 - n(chess & carom) + 4
n(chess & carom) = 10
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So, total number of students who play both chess & carom is = 10.
But there are 4 students who play all the three games.
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So, the number of students who play chess and carom but not table tennis is = 10-4 = 6.
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Ans: 6
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8) Aslam and Babul invested in a business in the ratio 3:2. Assume that 5 percent of total profit goes to workers' provident fund. If Aslam's share is Tk. 855000, what is the amount of total profit?
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Solution:
According to the question, 5% of total profit goes to WPF.
So, the remaining 95% of profit is distributed between Aslam and Babul.
.
Suppose,
Aslam's profit share is = 3x
So, Babul's profit share is = 2x
So, total profit after WPF deduction (i.e: 95% of total profit) = 3x+2x = 5x
.
According to the question:
3x = 855000
5x = 855000×5/3 = 1425000
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So, 95% of total profit = 1425000
100% of total profit = 1425000×100/95 = 1500000
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Ans: Tk. 1500000
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9) Alam invested an amount of Tk. 13900 divided in two different deposits at Bank X and Bank Y at the simple interest rate of 14 percent and 11 percent per annum, respectively. If the total amount of simple interest earned in two years is Tk. 3058, what was the amount invested in the deposit of Bank Y?
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Solution:
Suppose, the amount invested in Bank Y was = Tk. p
So, the amount invested in Bank X was = Tk. (13900-p)
.
According to the question:
2{14(13900-p)/100 + 11p/100} = 3058
(194600 - 14p + 11p)/100 = 1529
p = 13900
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Ans: Tk. 13900.
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10) Rashed is driving at a speed of 120 km per hour. Mahi started one hour late and started driving at a speed of 140 km per hour. How long will it take for Mahi to catch up Rashed?
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Solution:
When Mahi starts, Rashed is 120×1 = 120 km away from her.
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Relative speed of Mahi over Rashed = 140-120 kmph = 20 kmph.
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Required time to catch up Rashed = 120/20 hr = 6 hr.
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Ans: 6 hours.
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11) A table is three times as long as it is wide. If it were 5 feet shorter and 5 feet wider, it would be a square. How long and how wide is the table?
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Solution:
Let, the width of the table is x feet.
So, the length of the table is 3x feet.
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According to the question:
3x-5 = x+5
2x = 10
x = 5
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So, the length of the table is = 3×5 = 15 feet,
and the width of the table is = 5 feet.
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Ans: 15 feet, 5 feet.
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12) Given a = 3 + 2√2, find the value of (√a - 1/√a)
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Solution:
given, a = 3 + 2√2
or, a = 2 + 1 + 2√2 = (√2)² + 2×√2×1 + 1² = (√2 + 1)²
so, √a = (√2+1)
so, 1/√a = 1/(√2+1) = (√2-1)/{(√2+1)(√2-1)} = (√2-1)
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Therefore, √a - 1/√a = (√2+1) - (√2-1) = 2.
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Ans: 2.
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13) In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is Tk. 5600. The cost of 9 shirts, 9 pairs of trousers and 6 hats is Tk. 12900. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?
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Solution:
Suppose, the cost of a shirt is x, a pair of trousers is y and a hat is z.
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According to the question:
4x+4y+2z = 5600 -------------- (i)
9x+9y+6z = 12900 --------------- (ii)
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(i) × 2.25 => 9x+9y+4.5z = 12600 ------------ (iii)
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Subtracting (iii) from (ii) we get:
1.5z = 300
z = 200.
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Substituting hte value of z in (i) we get:
4x+4y + 2×200 = 5600
4x+4y = 5200
x+y = 1300
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So, x+y+z = 1300+200 = 1500.
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So, total cost of 1 shirt, 1 pair of trousers and 1 hat is Tk. 1500.
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Ans: Tk. 1500.
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