SONALI BANK –
SENIOR OFFICER – IT
WRITTEN MATHS
1) A boat takes 3 hours to travel to a certain
distance with the stream, and returns to the original place in 5 hours. How
long will it take to travel the same distance in stationary water? .
Solution: Suppose, the speed of the boat in stationary
water is p kmph, the rate of the stream is q kmph, and the distance is D km.
According to the question: p+q = D/3 ----------- (i) & p-q = D/5 -----------
(ii) (i) + (ii) => 2p = D/3 + D/5 = 8D/15 p = 4D/15 So, required time to
cover the distance in stationary water is = D/p = D/(4D/15) = 15/4 hrs = 3hrs
and 45mins.
Ans: 3 hours
and 45 minutes.
2) A man has Tk300000. He invests a part of the
amount at 8%, and the remaining amount at 10% p.a. At the end of the year he
earns a profit of Tk25600 from his entire investment. Find the amount he
invested under each rate.
Solution:
Suppose, he invested Tk P at 8% rate. So, he invested Tk (300000-P) at 10% rate.
According to the question: 0.08P + 0.1(300000-P) = 25600 0.08P + 30000 - 0.1P =
25600 0.02P = 4400 p = 4400/0.02 = 220000 So, he invested Tk220000 at 8% rate,
and Tk(300000-220000) or Tk80000 at 10% rate.
Ans:
Tk220000 at 8%, Tk80000 at 10%.
3)
M purchased a 30-inch TV whose height was 18 inches. If the size of a TV is
expressed as the lengths of its diagonal, find the width of the TV M purchased.
. Solution: Suppose, the width of the TV is = p inches. According to the
question: p² + 18² = 30² p² = 900 - 324 = 576 p = 24
Ans: 24 inches.
4) The ratio of the girls and boys in a
class was 2:5. If two new girls join the class, the ratio becomes 1:2. What was
the total number of students in the class?
Solution:
Suppose, there were 2p girls in the class. As the ratio of the girs and boys in
the class was 2:5, the number of boys in the class was = 2p × 5/2 = 5p
according to the question: (2p+2) : (5p) = 1 : 2 (2p+2)/(5p) = 1/2 5p = 4p + 4
p = 4 So, the total number of students in the class was = 2p+5p = 7p = 7×4 =
28. Ans: 28
5) How many liters of 15% salt solution
must be added to 5 liters of 8% salt solution to get a 10% salt solution?
Solution: Suppose, p liters of 15% should be
added. According to the question: (0.15p + 5×0.08)/(p+5) = 0.10 0.15p + 0.4 =
0.10p + 0.5 0.15p - 0.10p = 0.5 - 0.4 0.05p = 0.1 5p = 10 p = 2 Ans: 2 liters.