Test: Ratio and Proportion- 5 - Railways MCQ

D) 150
Explanation: Let number of students in 4 sections be A, B, C, D respectively. Then 1/2 of A = 1/3 of b = 1/4 of C = 1/5 of D So A : B : C : D = 2 : 3 : 4 : 5            [When A/2 = B/3 = C/4, then ratio A: B : C = 2 : 3 : 4] So students in 1st and 2nd section = [(2+3)/(2+3+4+5)] * 420 = 150

C) 18 : 20 : 21
Explanation: Previous ratio = 3 : 4 : 7 New ratio = (150/100) * 3 : (125/100) * 4 : (75/100) * 7

B) 8 : 9 : 7
Explanation: A gets = [7/(7+8+6)] * 4200 = 1400 B gets = [8/(7+8+6)] * 4200 = 1600 C gets = [6/(7+8+6)] * 4200 = 1200 Rs 200 added to each share, so new ratio = 1400+200 : 1600+200 : 1200+200
1600 : 1800 : 1400

A) Rs 66,240 Explanation: A/B = 15/16 and B/C = 17*18 So A : B : C = 15*17 : 16*17 : 16*18 = 255 : 272 : 288
So C’s salary = [288/(255+272+288)] * 1,87,450

D) Rs 30,000 Explanation: Ratio of last year income to this year income of A is 9 : 10. So income of A last year is 9x and this year is 10x.
Ratio of last year income to this year income of B is 13 : 15. So income of B last year is 13y and this year is 15y.
So ratio of the incomes of A and B last year was 9x : 13y Now given that ratio of the incomes of A and B last year was 9 : 13.
So 9x/13y = 9/13 This gives x = y Total of incomes of A and B this year = 10x+15y = 10x+15x = 25 x             (because x=y)So 25x = 50,000 This gives x = 2,000 So present income of B = 15y = 15x = 15*2000 = 30,000

B) 108, 144, 216
Explanation: 25 paise = 25/100 Rs, 50 paise = 50/100 Rs So value ratio of these coins become = 3*(25/100) : 4*(50/100) : 6*(1) = 3/4 : 2 : 6 = 3 : 8 : 24
So 25 paise coins value= [3/(3+8+24)] * 315 = Rs 27, so coins = 27 * (100/25) = 108
Similarly find others.

E) A, Rs 264 Explanation: New ratio = 1/2 : 1/4 : 1/7 = 14 : 7 : 4 So both ratio suggests that C has not gained any money, rather he has lose the money.
For both ratio find the shares of A and B With ratio 2 : 4 : 7, A gets = [2/(2+4+7)] * 650 = 100, B gets = [4/(2+4+7)] * 650 = 200
With ratio 14 : 7 : 4, A gets = [14/(14+7+4)] * 650 = 364, B gets = [7/(14+7+4)] * 650 = 182
B has also lose the money, A gain the money and = 364 – 100 = 264

B) 68 7/11%
Explanation: If 20% of boys and 45% of girls come by bus, then 80% of boys and 55% of girls opt transport other than bus.
Let total number of students in school = x So boys who opt other transport are (80/100) * 6/(6+5) * x = 24x/55 And girls who opt other transport are (55/100) * 5/(6+5) * x = x/4 So total students who opt other transport = (24x/55) + (x/4) = 151x/220 So required % = [(151x/220)/x] * 100 = 755/11 %

C) Rs 90,000 Explanation: Income of A = x, of B = 2x Expenditure of A = 2y, of B = 5y Savings is (income – expenditure). So x – 2y = 20,000 2x – 5y = 35,000 Solve the equations, x = 30,000 So total = x+2x = 3x = 3*30,000 = 90,000

B) Rs 2725 Explanation: When the shares reduce, the total amount will also reduce which is to be divided among them. So after reducing shares by Rs 10, Rs 15 and Rs 25 respectively, total amount is 5750 – (10+15+25) = 5700 So C’s share shall be [9/(4+6+9)] * 5700 = 2700 Actually C would have received = 2700 + 25

Answer – C.180 Explanation : 5x+6x+7x+ 18x = 180 X=10
Check 3x+4x+5x = 12x = 120 120+60 = 180

Answer – B.8:7 Explanation : Acid : 20    30 Water : 80  70 => 8:7

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

Answer – D.6:13 Explanation : 12x-5x =>7x = 21 X=21/7 =3
Present ratio = 15:36 After 3 years = 18:39 = 6:13

Answer – A.1:1 Explanation : 32000*12 : 48,000*8 = 32*12 : 42*8
384 : 384 = 1:1

Answer – C.Rs.37,500 Explanation : X=total profit 25/100*[x-7500] = 7500 x-7500 = 7500*100/25 =30,000 x = 37,500

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

Answer – D.3:2:1 Explanation : Speed = ½ : 1/3: 1/6 = 3/6:2/6:1/6
Time = 3:2:1

Answer – A.9000 Explanation : X’s saving = Expenditure of Y = S 4x-S + S = 12000 X = 3000
3x =3*3000 =  9000

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