২২৪৬১
If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?
উত্তর
500 miles
সমাধান
The initial position of the plane along with their final positions will make a right - angled triangle and the hypotenuse of that triangle will be the direct distance between them at 3 pm. Now, travel time from 1 pm to 3 pm is 2 hours.
So, distance covered towards North = 150 x 2 = 300 miles and towards west = 200 x 2 = 400 miles.
Therefore, their direct distance = (3002 + 4002)1/2 = (90000 + 160000)1/2 = 2500001/2 = 500 miles.
২২৪৬২
Son's age is now one-third of father's age. In twelve years from now son's age will be one half of the father's age. What is the son's age in years now?
উত্তর
12
সমাধান
x, 3x
2( x + 12) = 3x + 12
3x - 2x = 24 - 12
x = 12
২২৪৬৩
Sarah needs to make a cake and some coolies. The cake requires 3/8 cup of sugar and the coolies require 3/5 cup of sugar. Sarah has 15/16 cups of sugar. Does she have enough sugar, or how much more does she need?
উত্তর
needs 6/19 of a cup of sugar
সমাধান
Sugar required = 3/8 + 3/5 = (15 + 24) / 40 = 39/40 cup
Shortage of sugar = 39/40 - 15/16 = (78 - 75)/80 = 3/80 cup
২২৪৬৪
A man walked 2 miles east, then 2 miles south , then again 4 miles east and finally 10 miles north. How far did he walk from the starting point?
উত্তর
10
সমাধান
x2 = 62 + 82
x2 = 36 + 64
x2 = 100
x = 10
২২৪৬৫
Tanveer earns Tk. 5.00 for every hour he works. Last weeks worked for x hours. He purchased y kg of rice. Price of per kg rice is Tk. 12.00. He saved the remaining amount. which expression below shows his savings?
উত্তর
Tk. (5.00 x - 12.00y)
সমাধান
Tanveer earned Tk. 5.00 for every hour he worked, so his total earnings for last week can be expressed as 5x Tk.He purchased y kg of rice at Tk. 12.00 per kg, so the total cost of rice he purchased can be expressed as 12y Tk.His savings can be calculated by subtracting his total expenses from his total earnings, which gives:Savings = (Total earnings) - (Total expenses) = 5x - 12y TkTherefore, the expression that shows Tanveer's savings is 5x - 12y Tk.
২২৪৬৬
The ratio of boys and girls in a class is 1:2 and the class as 24 students. How many boys would have to be admitted to the class in order to make the ratio of boys to girls 1: 1?
উত্তর
8
সমাধান
Boys = 24 × 1 / 1 + 2 = 8
Girls = 16
Now, ( 8 + x) ; 16 = 1 : 1
gives x = 8
২২৪৬৭
If x5=243 , what is the value of x-3?
উত্তর
1/27
সমাধান
Here, x5 = 243
or, x5 = 35
or, x = 3
So, x - 3 = 3 - 3 = 1/33 = 1/27
২২৪৬৮
Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?
উত্তর
$306
সমাধান
Price at 15% off sale = 450 - 15% of 450 = 450 - 67.5 = $382.5
Price at additional 20% discount = 382.5 - 20% of 382.5 = 382.5 - 76.5 = $306
২২৪৬৯
A book sells for TK. 65. This price gives the seller a profit of 30% on his cost. What will be the new selling price if he cuts his profit to 10% of its cost?
উত্তর
55
সমাধান
At 30% profit , cost = Tk, ( 100×65)/130 = Tk.50
Now, At 10% profit , the new selling price = Tk.(110 × 50) 100 = Tk.55
২২৪৭০
A brand of paint costs Tk. 14 per liter and 1 liter of paint will cover an area of 150 square feet. what is the minimum cost of paint needed to cover the 4 walls of a rectangular room that ix 12 feet wide, 16 feet long and 8 feet high?
উত্তর
Tk. 42
সমাধান
Total surface area of the 4 walls = 2(length x height + width x height)
= 2(16 x 8 + 12 x 8) = 448 ft2
Total paint required = 448/150 ≈ 2.99 liter
Total cost of paint = 2.99 x 14 ≈ 42 TK