২১০০১
A person's present age is two-fifth of the age of his mother. After 8 years , he will be one-half of the age of his mother. How old is the mother at present?
উত্তর
40 years
সমাধান
A person's present age is two-fifth of the age of his mother. After 8 years , he will be one-half of the age of his mother . How old is the mother at present ?Let, present age of mother = xpresent age of the person or son = 2x/5After 8 year, mother's age = x+8son's age = 2x/5 + 8As per question,2x/5 + 8 = (x+8)/2or, (x+8)/2 - 2x/5 = 8or, x=40 So, present age of mother = 40 years (Ans:)
২১০০২
The ages of A and B are in the ratio 3:1. Fifteen years hence , the ratio will be 2:1. Their present ages are:
উত্তর
45 years , 15 years
সমাধান
Let the ages of A and B be 3x and x, respectively. Thenx + 153x + 15 = 12or 3x + 15 = 2x + 30⟹x = 15∴ A's age = 3×15 = 45yearsB's age = 15years
২১০০৩
Aunik, Kamal and Jamal invested TK. 8000, TK. 4000 and TK. 8000 respectively in a business. Aunik left after six months. If after eight months, there was a gain of TK. 4005, then what will be the share of Kamal?
উত্তর
TK. 890
সমাধান
Aunik's share=8000×6=48000 [as he left after 6 months]Kamal's share=4000×8=32000Jamal's share=8000×8=64000Ratio = 48000 : 32000 : 64000 = 48 : 32 : 64 = 3 : 2 : 4Total = 3+2+4 = 9Total profit = 4005∴ Kamal's profit = (2÷9) X 4005 = Tk. 890 (Ans:)
২১০০৪
15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take , if 3 women do as much work as 2 men?
উত্তর
30
সমাধান
3 women can do as much work as 2 men ∴ efficiency of women to do a piece of work, e2 = (1/3) ∴ efficiency of men to do a piece of work, e1 = (1/2) We know, Total work done = (no. of men or women) * (no. of days) * (no. of hours) * (efficiency) Therefore, m1 * d1 * h1 * e1 = m2 * d2 * h2 * e2 or, 15 * 21 * 8 * (1/2) = 21 * d2 * 6 * (1/3) or, d2 = 30 days
২১০০৫
A is 30% more efficient than B. How much time will they, working together , take to-complete a job which A alone could have done in 23 days?
উত্তর
13 days
সমাধান
Ratio of times taken by A and B = 100:130 = 10:13Suppose B takes x days to do the work.Then, 10:13 :: 23:x∴ x = 299/10A's 1 day's work = 1/23B's 1 day's work = 10/299(A+B)'s 1 day's work = (1/23 + 10/299) = 1/13Therefore, A and B together can complete the work in 13 days.
২১০০৬
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
উত্তর
144 min
সমাধান
Let the slower pipe alone fill the tank in x minThen, faster pipe will fill it in x/3 minSo, slower pipe in 1 minute can fill = 1/x part of the tankand faster pipe in 1 minute can fill = 3/x part of the tankagain, together in 1 minute can fill = 1/36 part of the tankAs per question,1/x + 3/x = 1/36∴ x = 144 min (Ans:)
২১০০৭
A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time , his speed (in km/hr ) must be:
উত্তর
12
সমাধান
Note: Half = One-half = 1/2One and a half = 1½ Here,one-half of the distance = 6 X ½ = 3 km | So, remaining distance = (6-3) = 3 kmtwo-thirds of the total time = 45 X ⅔ = 30 min | remaining time = (45-30) = 15 min∴ Speed = [∵ 1 hr = 60 min] = 12 km/hr (Ans:)
২১০০৮
How may seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
উত্তর
30
সমাধান
Here, Train Long is= 500m.Train Speed is =63*10003600=17.5 m/sec.Man Velocity is=3*10003600=0.83 m/secwe know, t=svso,Time required for Train pass 500m is=50017.5=28.57 Sec28.57 Sec Man pass the distance is= 0.83 X 28.57= 23.81 mTime Required for Train to pass 23.81 m distance is = 23.8117.5=1.36 SecSo, Time required for train to pass the man is= 28.57+1.36=29.93 say 30.00 Sec.Ans: 30 sec
২১০০৯
TK. 800 becomes TK. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will TK. 800 become in 3 years?
উত্তর
TK. 1052
সমাধান
The description field is required.
২১০১০
The percentage increase in the area of a rectangle , if each of its sides is increased by 20%, is:
উত্তর
44%
সমাধান
Let, one side of Rectangular is 100 mThe other side of Rectangular is 200 mSo, Present Area is = 100X200=20000 m2if increase 20% of both side of rectangular.Then, one side of Rectangular is= 100 +100×20100 = 120 m Other side of Rectangular is = 200 + 200×20100= 240 mAfter increasing the Rectangular area is = 120× 240 = 28800 m2increasing the Rectangular area is = 28800 - 20000 = 8800 m2So, % of increasing area is = 8800×10020000= 44%Ans: 44%.