২২৫৭১
A portion of the 7,200 is invested at a 4% annual return , while the remainder is invested at a 5% annual return. If the annual income from both portions is the same, what is the total income from the two investments?
উত্তর
Tk. 320
সমাধান
Let the investments be A and (7200 - A) respectively.
Interest, I = P n r
Now, A × 1 × 4/100 = (7200 - A) × 1 × 5/100
or, 4A = 5×7200 - 5A
or, 5A + 4A = 36000
or, 9A = 36000
or, A = 4000
So, total income = A × 1 × 4/100 + (7200 - A) × 1 × 5/100
= 4000×4/100 + (7200 - 4000)×5/100 = 160 + 160 = 320 TK
২২৫৭২
An empty swimming pool can be filled to capacity through an inlet pipe in 3 hours, and it can be completely drained by a drainpipe in 6 hours. If both pipes are fully open at the same time , in how many hours will the empty pool be filled to capacity?
উত্তর
6
সমাধান
Inlet pipe fill 1/3 part of the pool in 1 hour
Drain pipe drains 1/6 part of the pool in 1 hour
So, together they fill (1/3 - 1/6 = 1/6) part of the pool in 1 hour
So, together they will fill the pool completely in 6 hours
[Shortcut : (Inlet×Outlet) / (Outlet - Inlet) = (3×6) / (6 - 3) = 6 hr]
২২৫৭৩
A rectangular tank 10 inch by 8 inch by 4 inch is filled with water. If all of the water is to be transferred to cube-shaped tanks, each one 3 inches on a side, how many of these smaller tanks are needed?
উত্তর
12
সমাধান
Volume of the rectangular tank = 10×8×4 = 320 in3
Volume of a smaller tank = 33 = 27 in3
Number of smaller tanks needed = 320/27 ≈ 12
২২৫৭৪
Razia spent 3 hours climbing 6 miles up a hill. She spent 2 hours coming down the hill in a different path which had a length of 8 miles. For Razia's completed climb up and down the hil , what was her average speed, in miles per hour?
উত্তর
2.8
সমাধান
Average speed = total distance / total time = (6 + 8) / (3 + 2) = 14/5 = 2.8 miles/hr
২২৫৭৫
The length of a rectangle is 1 inch more than 2 times its width.The area of the rectangle is 36 square inches. what is the length of the rectangle?
উত্তর
9 inches
সমাধান
Let the width be W.
Then, Length = 2W + 1
Now, area, (2W + 1)×W = 36
or, 2W2 + W = 36
or, 2W2 + W - 36 = 0
or, 2W2 + 9W - 8W - 36 = 0
or, W(2W + 9) - 4(2W + 9) = 0
or, (2W + 9)(W - 4) = 0
or, W - 4 = 0 [2W + 9≠0]
or, W = 4
So, length, 2W + 1 = 2×4 + 1 = 9 inches
২২৫৭৬
A box contains 90 nuts each of 100 gms an d 100 bolts each of 150 gms. If the entire box weighs 35.5 kgs , then the wight of the empty box is--
উত্তর
11.5 kg
সমাধান
Weight of the nut and bolts = 90×100 + 100×150 = 9000 + 15000 = 2400gm = 24 kg
So, weight of the empty box = 35.5 - 24 = 11.5 kg
২২৫৭৭
Last year there were 1172 students at Gulshan High school. This year there are 15 percent more students than last year. Approximately how many students are at Gulshan High School this year?
উত্তর
1348
সমাধান
Number of students this year = 1172 + 15% of 1172 = 1172 + 175.8 ≈ 1348
২২৫৭৮
A wholesaler bought 1,200 radios for Tk. 18 each.The wholesaler sold 60 percent of the radios for Tk. 30 each and the rest for Tk. 15 each. what was the wholesaler's average profit per radio?
উত্তর
Tk. 6
সমাধান
Cost price = 1200×18 = 21600
Revenue = (60% of 1200)×30 + (40% of 1200)×15 = 21600 + 7200 = 28800
Profit = 28800 - 21600 = 7200
Profit per radio = 7200 / 1200 = 6 TK
২২৫৭৯
what is the original price of pack of milk powder which Zahid has bought for taka 100, after receiving a discount of 20%?
উত্তর
Tk. 125
সমাধান
Let the original price be A.
Then, A - 20% of A = 100
or, A - A/5 = 100
or, 4A/5 = 100
or, A = 100×5 / 4 = 125 TK
২২৫৮০
Saif , Noman and Morshed divided a sum of money among themselves in the ratio 2: 3: 7 Find the share of Saif if the total share of saif and Noman together is Tk. 1,500 less than that of Morshed.
উত্তর
Tk. 1,500
সমাধান
Let their shares be 2x, 3x and 7x respectively.
ATQ, 7x - (2x + 3x) = 1500
or, 7x - 5x = 1500
or, 2x = 1500
So, share of Saif is 1500 TK.