Ratio & Proportion Set 2

1. The students in 3 classes are in the ratio 3:4:5.If 20 students added in each class, the ratio becomes 5:6:7.Find the total no of students in all the 3 classes now ?
   A.160
   B.170
   C.180
   D.200
   E.None of these
   
   Answer – C.180
   Explanation :
   5x+6x+7x+ 18x = 180
   X=10
   Check 3x+4x+5x = 12x = 120
   120+60 = 180
   
   
   
2. Two equal containers are filled with water and acid. The concentration of acid in each container is 20% and 30%. What is the ratio of water in both the containers respectively ?
   A.7:8
   B.8:7
   C.6:4
   D.3:2
   E.None of these
   
   Answer – B.8:7
   Explanation :
   Acid : 20    30
   Water : 80  70 => 8:7
   
   
   
3. A horse takes 8 steps for every 5 steps of a fox, but 6 steps of a fox are equal to the 3 steps of the horse. What is the ratio of the speed of horse to the fox ?
   A.16:5
   B.20:19
   C.18:23
   D.17:21
   E.None of these
   
   Answer – B.16:5
   Explanation :
   6 step fox=3 step horse = 2:1
   16 step fox=8step horse=5 step fox
   16 step fox=5 step fox
   16:5
   
   
   
4. The ratio of age of Krish  and her mother is 5:12 and difference of their ages is 21. What will be the ratio of their ages after 3 years ?
   A.7:15
   B.11:5
   C.13:7
   D.9:13
   E.None of these
   
   Answer – D.6:13
   Explanation :
   12x-5x =>7x = 21
   X=21/7 =3
   Present ratio = 15:36
   After 3 years = 18:39 = 6:13
   
   
   
5. A started a business with Rs.32,000 after 4 months B joins with the business by investing Rs.48,000.At the end of the year, in what ratio should share their profit ?
   A.8:7
   B.7:6
   C.5:7
   D.9:5
   E.None of these
   
   Answer – A.1:1
   Explanation :
   32000*12 : 48,000*8 = 32*12 : 42*8
   384 : 384 = 1:1
   
   
   
6. A working partner gets 25% as his commissions after his commissions paid  that is equal to Rs.7500, then what is the total profit ?
   A.Rs.32,000
   B.Rs.30,000
   C.Rs.37,500
   D.Rs.40,000
   E.None of these
   
   Answer – C.Rs.37,500
   Explanation :
   X=total profit
   25/100*[x-7500] = 7500
   x-7500 = 7500*100/25 =30,000
   x = 37,500
   
   
   
7. Equal quantities of 3 mixtures of milk and water are mixed in the ratio 1:3, 2:3 and 3:4.The ratio of water and milk in the new mixture is
   A.45:76
   B.151:269
   C.123:154
   D.145:245
   E.None of these
   
   Answer – B.151:269
   Explanation :
   Milk = 1/4 : 2/5 :3/7
   = 35/140 :56/140 : 60/140
   Quantity of milk in new mix = 35+56+60 = 151
   Quantity of water in new mix = 140*3 = 420-151 = 269
   M:W = 151:269
   
   
   
8. The speed of P, Q and R are in the ratio of 2:3:6, what is the ratio of time taken by each one of them for the same distance ?
   A.5:7:2
   B.3:2:4
   C.1:2:3
   D.3:2:1
   E.None of these
   
   Answer – D.3:2:1
   Explanation :
   Speed = ½ : 1/3: 1/6
   = 3/6:2/6:1/6
   Time = 3:2:1
   
   
   
9. The ratio of income of X and Y is 4:3. The sum of their expenditure is Rs.12,000 and the amount of savings is X is equal to the amount of expenditure of Y.What is the salary of  Y?
   A.9000
   B.7000
   C.12000
   D.15000
   E.None of these
   
   Answer – A.9000
   Explanation :
   X’s saving = Expenditure of Y = S
   4x-S + S = 12000
   X = 3000
   3x =3*3000 =  9000
   
   
   
10. When 7 is added to the numerator and denominator of the fraction, then the new ratio of numerator and denominator becomes 13:19, what is the original ratio ?
    A.11:13
    B.7:9
    C.4:7
    D.Can’t be determined
    E.None of these
    
    Answer – D.Can’t be determined
    Explanation :
    X+7/y+7 = 13/19 x and y are different variable ,so original fraction cannot be determined

Ratio & Proportion Set 1 

1. Find out the third proportion of the term 12 and 24
   A)38
   B)44
   C)48
   D)42
   
   C)48
   Explanation :
   12:24 :: 24 : ?
   ? = (24*24)/12 = 48
   
   
   
2. If a:b = 2:3, b:c = 6:5 and c:d = 3:5 then find the value of a:b:c:d
   A)18:25:12:18
   B)12:18:15:25
   C)25:18:15:12
   D)12:25:18:25
   
   B) 12:18:15:25
   Explanation :
   a:b = 2:3 = 12:18
   b:c = 6:5 = 18:15
   c:d = 3:5 = 15 :25
   a:b:c:d = 12:18:15:25
   
   
   
3. If x:y = 4:7, the  value of (x2 + y2) /(x2 – y2) = ?
   A)-33/65
   B)65/33
   C)33/65
   D) -65/33
   
   D) -65/33
   Explanation :
   X = 4a; y = 7a
   (x2 + y2) /(x2 – y2) = (4a)2 + (7a)2/ (4a)2 – (7a)2
   = a2(16+49)/ a2(16-49)
   = -65/33
   
   
   
4. The ratio of boys and girls in the school is 7:9 when 22 new boys  are joined in this school  then the ratio become 9:10.How many girls in this school ?
   A)180
   B)200
   C)160
   D)220
   
   A)180
   Explanation :
   7x+22/9x = 9/10
   70x+220 = 81x
   11x = 220
   X =20
   20*9 = 180 girls(7B:9G)
   
   
   
5. Two numbers are in the ratio of 5:8 .If 4 is subtracted from each then the ratio become 1:2.The small number is
   A)16
   B)4
   C)10
   D)2
   
   C)10
   Explanation :
   5x-4/8x-4 = ½
   10x-8 = 8x-4
   2x = 4
   X=2
   5(2) = 10
   
   
   
6. x:y = 7:4 then (4x+7y) : (7x+4y)
   A)65:56
   B)56:65
   C)34:45
   D)13:18
   
   B)56:65
   Explanation :(4(7)+7(4)) : (7(7)+4(4)) = 56:65
   
   
   
7. The sum of present age of 2 persons is 100yrs.Before 5 years the ratio of their ages is 5:13.Find the age of younger person
   A)15
   B)20
   C)25
   D)30
   
   D)30
   Explanation :
   From option
   30+70 = 100
   25:65 = 5:13
   
   
   
8. The ratio of monthly income of A and B in the ratio is 6:5 and the ratio of their expenditure is 9:7.If each saves Rs.1500.Then the sum of their salary is
   A)11,000
   B)9,000
   C)1,0000
   D)12,000
   
   A)11,000
   Explanation :
   4500:3500 – e
   1500:1500 – s
   6000 + 5000 = 11000
   
   
   
9. What number should be added or subtracted from each term in the ratio 11:9 so that it become 6:5
   A)+4
   B)-4
   C)-5
   D)-3
   
   A)+4
   Explanation :
   44:36
   Add 4
   48:40 = 6:5
   
   
   
10. The ratio of two persons A and B salaries in the ratio 12:7 if 12% increased salary yearly then what will be the B Salary after 2 yrs.
    A)7808
    B)8700
    C)7,500
    D)8781
    
    D)8781
    Explanation :
    12:7 = 12,000 : 7,000
    12% =  B = 840……1st yr and B = 941 …..2nd yr
    New inc B  = 7000+840+941 = 8781

 

Compound Interest Set 2:

1. The difference between the total simple interest and the total compound interest compounded annually at the same rate of interest on a sum of money at the end of two years is Rs. 350. What is definitely the rate of interest per cent per annum?
   A.9,300
   B.7600
   C.12000
   D.Data inadequate
   E.None of these
   
   Answer – D.Data inadequate
   Explanation :
   Difference = Pr2/(100)2
   = (350×100×100)/(P×r2)
   P is not given
   
   
   
2. Aswin invested an amount of Rs.9000 in a fixed deposit scheme for 2 years at CI rate 6% pa. How much amount will Aswin get on maturity of the fixed amount ?
   A.Rs.11,230
   B.Rs.10,250
   C.Rs.10,112
   D.Data inadequate
   E.None of these
   
   Answer – C.Rs.10,112
   Explanation :
   Amount = 9000*106/100*106/100
   = 9000*53/50*53/50
   = 10,112
   
   
   
3. A sum of money invested for 7years in Scheme 1 which offers SI at a rate of 8% pa. The amount received from Scheme 1 after 7 years invested for 2 years in Scheme 2 which offers CI rate of 10% pa. If the interest received from Scheme B was Rs.1638. What was the sum invested in Scheme 1 ?
   A.Rs.7500
   B.Rs.5000
   C.Rs.8200
   D.Rs.9000
   E.None of these
   
   Answer – B.Rs.5000
   Explanation :
   SI =>Amount = x*8*7/100 + x = 56x+100x/100 = 156x/100 = 39x/25
   CI=> 39x/25[(1+10/100)2 – 1]
   1638 = 39x/25[121/100 – 1] = 39x/100[21/100]
   X = 1638*100*25/21*39 = 5000
   
   
   
4. Rs.5200 was partly invested in Scheme A at 10% pa CI for 2 years and Partly invested in Scheme B at 10% pa SI for 4 years. Both the schemes earn equal interests. How much was invested in Scheme A ?
   A.Rs.1790
   B.Rs.2200
   C.Rs.3410
   D.Rs.2670
   E.None of these
   
   Answer – C.Rs.3410
   Explanation :
   Amount invested in Scheme B = X
   Amount invested in Scheme A = 5200 – x
   X*10*4/100 = (5200-x)*21/100……………………[(1-10/100)2-1] = 21/100
   40x/100 = (5200-x)*21/100
   2x/5 = (5200-x)*21/100
   200x = 5200*21*5 – x*5*21
   200x = 546000 – 105x
   305x = 546000
   X = 1790
   Scheme A = 5200 – 1790 = 3410
   
   
   
5. The CI on Rs.7000 for 3 years at 5% for first year, 7% for second year, 10% for the third year will be
   A.Rs.1800
   B.Rs.1530
   C.Rs.1651
   D.Rs.2050
   E.None of these
   
   Answer – C.Rs.1651
   Explanation :
   A = 7000*105/100*107/100*110/100
   = 7000*1.05*1.07*1.1
   = 8650.95 = 8651
   CI = 8651-7000 = 1651
   
   
   
6. Poorni and Priyanka have to clear their respective loans by paying 2 equal annual instalments of Rs.20000 each. Poorni pays at 10% pa of SI and Priyanka pays at 10% CI pa. What is the difference in their payments ?
   A.200
   B.300
   C.400
   D.500
   E.None of these
   
   Answer – A.200
   Explanation :
   D =[(20,000 *110/100*110/100) – 20,000]  – 20,000 *10*2/100
   =[ 24200-20000]-4000
   =4200 – 4000
   D = 200
   
   
   
7. A sum of Rs.3,50,500 is to be paid back in 2 equal annual instalments. How much is each instalment, if the rate of interest charged 4% per annum compound annually ?
   A.Rs.1,90,450
   B.Rs.1,65,876
   C.Rs.1,76,545
   D.Rs.1,85,834
   E.None of these
   
   Answer – D.Rs.1,85,834
   Explanation :
   Total value of all the 3 instalments
   [X*100/104] + [X*100*100/104]  = 3,50,500
   X*25/26 + x*625/676 = 3,50,500
   X*25/26[1+25/26] = 3,50,500
   X*25/26[51/26] = 3,50,500
   X = 3,50,500*676/25*51 = 1,85,833.72 = 1,85,834
   
   
   
8. At CI, if a certain sum of money is doubled in 4 years, then the amount will be four fold in how many years ?
   A.7years
   B.4years
   C.10years
   D.8years
   E.None of these
   
   Answer – D.8years
   Explanation : 2n = 2*4 = 8 years
   
   
   
9. X has lent some money to A at 5% pa and B at 8% pa. At the end of the year he has gain the overall interest at 7% pa.In what ratio has he lent the money to A and B ?
   A.2:1
   B.1:2
   C.3:1
   D.1:4
   E.None of these
   
   Answer – B.1:2
   Explanation :
   5………………………….8
   ……………7…………….
   1………………………….2
   Ratio A : B = 1:2
   
   
   
10. The difference between interest received by X and Y is Rs.315 on Rs.3500 for 3 years. What is the difference in rate of interest ?
    A.1.5%
    B.2%
    C.3%
    D.2.7%
    E.None of these
    
    Answer – C.3%
    Explanation :
    3500*3/100(R1-R2) = 315
    R1-R2 = 315*100/10500 = 3%

Compound Interest Set 1

1. On a certain sum of money, after 2 years the simple interest and compound interest obtained are Rs 800 and Rs 960 respectively. What is the sum of money invested?
   A) Rs 1420
   B) Rs 1325
   C) Rs 1000
   D) Rs 1405
   E) Rs 1375
   
   C) Rs 1000
   Explanation:
   Diff = 960-800 = 160
   r = 2*Diff*100/SI
   So r = 2*160*100/800 = 40%
   Now 160 = Pr2/1002
   
   
   
2. Rs 6000 becomes Rs 7200 in 3 years at a certain rate of compound interest. What will be the amount received after 9 years?
   A) Rs 11,498
   B) Rs 10,352
   C) Rs 9,368
   D) Rs 10,368
   E) None of these
   
   D) Rs 10,368
   Explanation:
   6000[1 + r/100]3 = 7200
   So [1 + r/100]3 = 6/5
   So 6000[1 + r/100]9 = 6000*(6/5)*(6/5)*(6/5)
   
   
3. A man borrows Rs 4000 at 8% compound interest for 3 years. At the end of each year he paid Rs 500. How much amount should he pay at the end of 3rd year to clear the debt?
   A) Rs 4254.5
   B) Rs 3465.2
   C) Rs 3485.2
   D) Rs 4345.4
   E) Rs 3915.6
   
   E) Rs 3915.6
   Explanation:
   Amount after 1 yr = 4000[1 + 8/100] = 4320
   Paid 500, so P = 4320 – 500 = 3820
   Amount after 2nd yr = 3820[1 + 8/100] = 4125.6
   So P= 4125.6-500 = 3625.6
   Amount after 3rd yr = 3625.6[1 + 8/100] = 3915.6
   
   
   
4. A sum of money is lent for 2 years at 20% p.a. compound interest. It yields Rs 482 more when compounded semi-annually than compounded annually. What is the sum lent?
   A) Rs 25,600
   B) Rs 20,000
   C) Rs 26,040
   D) Rs 40,500
   E) None of these
   
   B) Rs 20,000
   Explanation:
   P[1 + (r/2)/100]4 – P[1 + r/100]2 = 482
   P[1 + 10/100]4 – P[1 + 20/100]2 = 482
   Solve, P = 20,000
   
   
5. The compound interest obtained after 1st and 2nd year is Rs 160 and Rs 172.8 respectively on a certain sum of money invested for 2 years. What is the rate of interest?
   A) 10%
   B) 8%
   C) 8.5%
   D) 9%
   E) 9.2%
   
   B) 8%
   Explanation:
   Difference in interest for both yrs = 172.8 – 160 = 12.8
   So (r/100)*160 = 12.8
   
   
   
6. A sum of money becomes Rs 35,280 after 2 years and Rs 37,044 after 3 years when lent on compound interest. Find the principal amount.
   A) Rs 32,000
   B) Rs 28,000
   C) Rs 31,500
   D) Rs 32,500
   E) None of these
   
   A) Rs 32,000
   Explanation:
   P[1 + r/100]3 = 37,044, and P[1 + r/100]2 = 35,280
   Divide both equations, [1 + r/100] = 37044/35280 = 21/20
   So P[21/20]2 = 35280
   
   
7. The difference between compound interest earned after 3 years at 5% p.a. and simple interest earned after 4 years at 4% p.a. is Rs 76. Find the principal amount.
   A) Rs 32,000
   B) Rs 28,000
   C) Rs 31,500
   D) Rs 32,500
   E) None of these
   
   A) Rs 32,000
   Explanation:
   [P[1 + 5/100]3 – P] – P*4*4/100 = 76
   P [9261/8000 – 1 – 16/100] = 76
   
   
8. A sum of money is lent at simple interest and compound interest. The ratio between the difference of compound interest and simple interest of 3 years and 2 years is 35 : 11. What is the rate of interest per annum?
   A) 20 3/4%
   B) 17 2/5%
   C) 18 2/11%
   D) 22 1/5%
   E) 24 5/6%
   
   C) 18 2/11%
   Explanation:
   Difference in 3 yrs = Pr2(300+r)/1003
   Difference in 2 yrs = Pr2/1002
   So Pr2(300+r)/1003 / Pr2/1002 = 35/11 (300+r)/100 = 35/11
   
   
9. A sum of money borrowed at 5% compound interest is to paid in two annual installments of Rs 882 each. What is the sum borrowed?
   A) Rs 1650
   B) Rs 2340
   C) Rs 2630
   D) Rs 1640
   E) Rs 2640
   
   D) Rs 1640
   Explanation:
   P = 882/[1 + 5/100] + 882/[1 + 5/100]2
   
   
10. Rs 3903 is to be divided in a way that A’s share at the end of 7 years is equal to the B’s share at the end of 9 years. If the rate of interest is 4% compounded annually, find A’s share.
    A) Rs 2475
    B) Rs 1875
    C) Rs 2175
    D) Rs 1935
    E) Rs 2028
    
    B) Rs 1875
    Explanation:
    A’s share = (1 + 4/100)7
    B’s share = (1 + 4/100)9
    Divide both, B/A = (1 + 4/100)2 = 676/625
    So A’s share = 625/(676+625) * 3903