Quant Boosters  Maneesh  Set 3

2A = 3B = 5C
A : B = 3:2
B:C = 5:3
A:B:C = 15:10:6
A’s share = 1550 * 15/(15+10+6) = 50 * 15 = Rs.750

Q5) Raju, Ravi and Ramu invest Rs.15000, Rs.25000 and Rs.30000 respectively in a business. After one year Raju removed his money but Ravi and Raju continued for one more year. If the net profit after 2 years is Rs.25200, then Raju’s share in the profit is:

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?