২২৫৯১
A general wishing to draw up his 7250 men in the form of a solid square found that he had 95 men over. What is the number of men in the front row?
উত্তর
None
২২৫৯২
Divide Rs. 5625 among A, B & C so that A may receive 1/2 as much as B & C and B 1/4 of what A and C together receive?
উত্তর
1875, 1125, 2625
সমাধান
Let they receive A, B & C Rs. respectively.
Now, A = (B + C) / 2
or, 2A = B + C - - - - - - - - - - (i)
Again, B = (A + C) / 4
or, 4B = (A + C)
or, 4B = (B + C) / 2 + C
or, 4B = B/2 + C/2 + C
or, 4B - B/2 = 3C/2
or, 7B/2 = 3C/2
or, B = 3C/7 - - - - - - - (ii)
Now, 2A = 3C/7 + C [from (i)]
or, 2A = 10C/7
or, A = 5C/7 - - - - - - (iii)
From (ii) and (iii),
B : C = 3 : 7
C : A = 7 : 5
So, A : B : C = 5 : 3 : 7
A will receive = 5 / (5 + 3 + 7) × 5625 = 1875 Rs.
B will receive = 3 / (5 + 3 + 7) × 5625 = 1125 Rs.
C will receive = 7 / (5 + 3 + 7) × 5625 = 2625 Rs.
২২৫৯৩
Business partnera A, B and C agree to divide their total profit for the year in the ratios 4: 7: 8 respectively. If A's share of the profit is Rs. 16,000, what was the total profit of the business partners for the year?
উত্তর
Rs. 76,000
সমাধান
Let the total profit be P.
Now, A's share of profit, 4 / (4 + 7 + 8) × P = 16000
or, 4P/19 = 16000
or, P = 16000 × 19 / 4 = 76000 Rs.
২২৫৯৪
If Rs. 450/- amount to Rs. 504/- in three years at simple interest, what will Rs. 650/- amount in 2 years & 6 months the interest rate being the same in both cases?
উত্তর
Rs. 715/-
সমাধান
Here, 2 year 6 months = 2.5 years
Principal with simple interest, A = P( 1 + n r)
Now, 504 = 450( 1 + 3 × r)
or, 1 + 3r = 504/450
or, 3r = 504/450 - 1
or, 3r = (504 - 450) / 450
or, 3r = 54 / 450
or, r = 54 / (450 × 3)
or, r = 1/25
Again, A = 650( 1 + 2.5 × 1/25)
or, A = 650 × (25 + 2.5)/25
or, A = 650 × 27.5 / 25
So, A = 715 Rs.
২২৫৯৫
A glass when full of milk, weighs one kilogram. When half full, it weighs 3/4 kilogram. What is the weight of the empty glass?
উত্তর
.5 kg
সমাধান
Weight of 1/2 glass of milk = 1 - 3/4 = 1/4 kg
So, weight of full glass of milk = 2 × 1/4 = 1/2 kg
So, weight of the glass = 1 - 1/2 = 1/2 kg = 0.5 kg
২২৫৯৬
In a right angled triangle the horizontal side measures 8 cm and the vertical side measures 12 cm. What is the area of the triangle?
উত্তর
48 sq cm
সমাধান
Area of triangle = 1/2 × base × height = 1/2 × 8 × 12 = 48 cm2
২২৫৯৭
Complete the series 4, 9, 17, 35,------
উত্তর
69
সমাধান
4 × 2 + 1 = 9
9 × 2 - 1 = 17
17 × 2 + 1 = 35
35 × 2 - 1 = 69
২২৫৯৮
Complete the series 1, 9, 17, 25, 33------
উত্তর
41
সমাধান
1 + 8 = 9
9 + 8 = 17
17 + 8 = 25
25 + 8 = 33
33 + 8 = 41
২২৫৯৯
If 12 years are added to 2/3 age of Rani, she will be three years older than today. What is Rani's present age?
উত্তর
27
সমাধান
Let the present age of Rani be R.
Now, 2R/3 + 12 = R + 3
or, R - 2R/3 = 12 - 3
or, R/3 = 9
or, R = 27 years
২২৬০০
A man travels 100 miles at 20 miles per hour, 60 miles at 30 miles per hour and 80 miles at 10 miles per hour, what is his average rate for the three trips?
উত্তর
16 miles per hr
সমাধান
Time travelled at 20 miles//hr = 100/20 = 5 hrs
Time travelled at 30 miles//hr = 60/30 = 2 hrs
Time travelled at 10 miles//hr = 80/10 = 8 hrs
Total time travelled = 5 + 2 + 8 = 15 hrs
Total travelled = 100 + 60 + 80 = 240 miles
Average rate = 240 / 15 = 16 miles per hour