Quant Boosters  Maneesh  Set 3

Number of Questions  30
Topic  Quant Mixed Bag
Solved ?  Yes
Source 

Q1) A and B start a business. A invests Rs.600 more than B for 4 months and B for 5 months. A’s share is Rs.48 more than that of B out of a total profit of Rs.528. Find the capital contributed by each?

A’s profit + B’s profit = 528
B’s profit +B’s profit+48 = 528
2 * B’s profit = 480
B’s profit = 240; A’s profit = 288
A’s capital * 4/B’s capital * 5 = 288/240 = 6/5
A’s capital/B’s capital = 6/4 = 3/2
B’s capital + 600/B’s capital = 3/2
2 * B’s capital +1200 = 3* B’s capital
B’s capital = Rs.1200; A’s capital = Rs.1800

Q2) Two partners invested Rs.1250 and Rs.850 respectively in a business. They decided to distribute equally 60% of the profit and the remaining as the interest on their capital. If one receives Rs.320 more than the other, find the total profit.

Let x is total profit.
Both partners will get 0.3x each.
Remaining 0.4x will be divided in the ratio of 1250/850 => 25/17
One will get 0.3x+ (10x/42) and other will get 0.3x+(6,8x/42)
22.6x/42 – 19.4x/42 = 320
3.2x = 42 * 320
X = 4200
Hence total profit is Rs.4200.

Q3) A and B enter in to a partnership. A puts in Rs.2000 but at the end of three months, withdraws Rs.500 and again at the end of 8 months withdraws Rs.300. Out of a total profit of Rs.900 at the end of the year, B’s share was Rs.400. Find B’s capital.

A’s profit/B’s profit = 5/4
A’s capital = 2000*3 + 1500 * 5 +1200 *4 = 6000+7500+4800 = 18300
A’s capital/ B’s capital = 5/4
B’s capital for 12 months= 4 * 18300/5 = 4 * 3660 = 14640
B’s capital for one month = 14640/12 = Rs.1220

Q4) A, B and C started a business, two times of A’s capital is equal to 3 times of B’s capital and equal to 5 times of C’s capital. Out of a profit of Rs.1550, A’s share is

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)