A school has 4 sections of class 12, such that half the number of students of 1st section, 1/3rd of 2nd section, 1/4th of 3rd section and 1/5th of the 4th section are equal. If total number of students in class 12 is 420, find the number of students in sections 1st and 2nd.
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
The income of A, B, and C are in the ratio 3 : 4 : 7. If their incomes be changed such that the new income of A is 50% increased, 25% increased for B and 25% decrease for C. Find the ratio of their new incomes.
C) 18 : 20 : 21
Explanation: Previous ratio = 3 : 4 : 7 New ratio = (150/100) * 3 : (125/100) * 4 : (75/100) * 7
A, B and C divide Rs 4200 among themselves in the ratio 7 : 8 : 6. If Rs 200 is added to each of their shares, what is the new ratio in which they will receive the money?
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
The ratio of the monthly salaries of A and B is in the ratio 15 : 16 and that of B and C is in the ratio 17 : 18. Find the monthly income of C if the total of their monthly salary is Rs 1,87,450.
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
The ratio of the incomes of A and B last year was 9 : 13. Ratio of their incomes of last year to this year is 9 : 10 and 13 : 15 respectively. The sum of their present incomes is Rs 50,000. What is the present income of B?
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
A sum of Rs 315 consists of 25 paise, 50 paise and 1 Re coins in the ratio 3 : 4 :6. What is the number of each kind of coin respectively?.
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.
Rs 650 was divided among 3 children in the ratio 2 : 4 : 7. Had it been divided in the ratio 1/2 : 1/4 : 1/7, who would have gained the most and by how much?
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
The ratio of the number of boys to the number of girls in a school is 6 : 5. If 20% of boys and 45% of girls come by bus to school, what percentage of students opt transport other than bus to come to school?
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 %
The incomes of A and B are in the ratio 1 : 2 and their expenditures are in the ratio 2 : 5. If A saves Rs 20,000 and B saves Rs 35,000, what is the total income of A and B?
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
Rs 5750 is divided among A, B, and C such that if their share be reduced by Rs 10, Rs 15 and Rs 25 respectively, the reminder amounts with them shall be in the ratio 4 : 6 : 9. What was C’s share then?
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
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 ?
Answer – C.180 Explanation : 5x+6x+7x+ 18x = 180 X=10
Check 3x+4x+5x = 12x = 120 120+60 = 180
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 ?
Answer – B.8:7 Explanation : Acid : 20 30 Water : 80 70 => 8:7
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 ?
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
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 ?
Answer – D.6:13 Explanation : 12x5x =>7x = 21 X=21/7 =3
Present ratio = 15:36 After 3 years = 18:39 = 6:13
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 ?
Answer – A.1:1 Explanation : 32000*12 : 48,000*8 = 32*12 : 42*8
384 : 384 = 1:1
A working partner gets 25% as his commissions after his commissions paid that is equal to Rs.7500, then what is the total profit ?
Answer – C.Rs.37,500 Explanation : X=total profit 25/100*[x7500] = 7500 x7500 = 7500*100/25 =30,000 x = 37,500
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
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 = 420151 = 269 M:W = 151:269
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 ?
Answer – D.3:2:1 Explanation : Speed = ½ : 1/3: 1/6 = 3/6:2/6:1/6
Time = 3:2:1
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?
Answer – A.9000 Explanation : X’s saving = Expenditure of Y = S 4xS + S = 12000 X = 3000
3x =3*3000 = 9000
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 ?
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
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