Quant Boosters  Maneesh  Set 3

Raju’s capital = 1 * 15000 = 15000
Ravi’s capital = 2 * 25000 = 50000
Ramu’s capital = 2 * 30000 = 60000
Raju’s share = 25200 * 15000/125000 = 25200 * 3/25 = 1008 * 3 = Rs.3024

Q6) Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. Find the sum placed on simple interest.

Let Principal is P
P * 3 * 8/100 = 1/2(4000(110/100)^24000)
6P/25 = 1/2(40 * 121 4000) = 1/2(48404000) = 1/2 (840) = 420
P = 25 * 420/6 = 25 * 70 = 1750

Q7) Find the difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned halfyearly?

P = 1200 N = 1 YEAR R= 10%
SI = 1200 * 1 * 10/100 = 120 RS
CI = 1200(1+(10/2)/100)^2 – 1200
= 1200 * 441/400 1200
= 1200 * (441/400 – 1)
= 1200 * 41/400
= 123 RS
Difference = 3RS

Q8) The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?

(15000(1+R/100) ^215000) – 15000 * 2 * R/100 = 96
15000((1+R/100) ^21 2R/100) = 96
15000(1+2R/100+R^2/1000012R/100) = 96
15000 * R^2/10000 = 96
3R^2 = 192
R^2 = 64
R = 8%

Q9) The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. Find the sum.

Let P = 1 Rs
SI = 1 * 2 * 4/100 = 2/25
CI = 1 * (104/100)^2 – 1 = 676/6251 = 51/625
CISI = 51/625 – 2/25
= 5150/625 = 1/625
Hence for 1 Rs sum difference is 1/625 Rs
So for getting 1 Rs difference Sum will be 625 Rs.

Q10) The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. Find the period (in years)

Total Amount = 30000+4347 = 34347
34347 = 30000 * (1+7/100) ^N
(107/100)^N = 34347/30000 = 11449/10000
(107/100)^N = 11449/10000
N = 2 Years

Q11) Ram’s speed is with the current is 10 m/s and speed of current is 2 m/s .Then What’s Ram’s speed against current?

Let speed of current y = 2 m/s
Let Ram’s speed in still water is x m/s
x+2 = 10 m/s
x = 8 m/s

Q12) A boat can travel with a speed of 15 m/s in still water. If the speed of the stream is 5 m/s, find the time taken by the boat to go 100 m downstream?

x = 15 m/s
y= 5 m/s
downstream speed ,d = 15+5 = 20 m/s
distance = 100 m
time taken = 100/20 = 5 seconds

Q13) A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours and 30 minutes. Find the speed of the stream?

x = 15 km/hr
t = 4 1/2 h = 9/2 hours
9/2 = 30/15+y + 30/15  y where y is speed of stream
9/2 = 30(30)/225y^2
225y^2 = 900 * 2/9 = 200
y^2 = 25
y = 5 km/hr

Q14) A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

D/xy = 8 4/5 = 44/5
D/x+y = 4
x+y/xy = 44/20
20x+20y = 44x 44y
24x = 64y
x/y = 64/24 = 8/3

Q15) A boat takes 90 minutes less to travel 36 km downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 kmph, find the speed of the stream?