Tips, tricks and formula on Ratio and Proportion
1) What is the fourth proportional to the numbers 2, 5, 8.
a) 40b) 20
c) 15
d) 10
ANSWER : 20
Solution :
2/5 = 8/x ; x = 40/2 = 20
Solution :
2/5 = 8/x ; x = 40/2 = 20
2) The third proportional to 3.5, 5.6 is:
a) 7.1b) 9.1
c) 8.96
d) 4.55
ANSWER : 8.96
Solution :
3.5/5/6 = 5.6/x ; x = 5.6 * 5.6 / 3.5 = 8.96
Solution :
3.5/5/6 = 5.6/x ; x = 5.6 * 5.6 / 3.5 = 8.96
3) The addition of two numbers is m and their quotient is y/z. The two numbers are:
a) y, zb) my/z, mz/y
c) m/(y + z), m/(y – z)
d) my/(y + z), mz/(y + z)
ANSWER : my/(y + z), mz/(y + z)
Solution :
Let the numbers be a and b.
Therefore, (a+b) = m; a/b = y/z
a = yx, b = zx
(a+b) = (yx + zx) = (y+z)x = m
Therefore, x = m/(y+z)
Hence, a = my/(y+z); b = mz/(y+z)
Solution :
Let the numbers be a and b.
Therefore, (a+b) = m; a/b = y/z
a = yx, b = zx
(a+b) = (yx + zx) = (y+z)x = m
Therefore, x = m/(y+z)
Hence, a = my/(y+z); b = mz/(y+z)
4) M:N = 3:4, N:O = 5:7 and O:P = 7:9. Then M:P =?
a) 1/3b) 7/9
c) 5/12
d) None of these
ANSWER : 5/12
Solution :
M/P = M/N * N/O * O/P = ¾ * 5/7 * 7/9 = 5/ 12
Solution :
M/P = M/N * N/O * O/P = ¾ * 5/7 * 7/9 = 5/ 12
5) If X:Y = 2:3, Y:Z = 4:5. Find X:Y:Z.
a) 2:3:5b) 8:12:15
c) 2:8:5
d) 2:7:5
ANSWER : 8:12:15
Solution :
If A:B = m1:n1 ; B:C = m2:n2
Then, A:B:C = (m1*m2):(n1*m2):(n1*n2)
Therefore, X:Y:Z = (2*4):(3*4):(3*5)
= 8:12:15
Solution :
If A:B = m1:n1 ; B:C = m2:n2
Then, A:B:C = (m1*m2):(n1*m2):(n1*n2)
Therefore, X:Y:Z = (2*4):(3*4):(3*5)
= 8:12:15
6) If the ratio of present ages of Jeet and Jay is 5:7 and after 6 years the ratio will be 3:4, what is the present age of Jay?
a) 42b) 30
c) 36
d) None of these
ANSWER : 42
Solution :
As the present age of Jeet and Jay are in the ratio 5:7, let their ages be 5x and 7x respectively.
Therefore, their ages after 6 years will be (5x+6) and (7x+6) respectively.
Now, it is given that (5x+6)/(7x+6) = 3/4
4*(5x+6) = 3*(7x+6)
x = 6
Hence, the present age of Jay is 7x = 7*6 = 42 years
Solution :
As the present age of Jeet and Jay are in the ratio 5:7, let their ages be 5x and 7x respectively.
Therefore, their ages after 6 years will be (5x+6) and (7x+6) respectively.
Now, it is given that (5x+6)/(7x+6) = 3/4
4*(5x+6) = 3*(7x+6)
x = 6
Hence, the present age of Jay is 7x = 7*6 = 42 years
7) Find the value of x when y = 5, if x varies directly as 4y-1 and x = 14 when y = 2.
a) 38b) 35
c) 10
d) 28
ANSWER : 38
Solution :
Let z = 4y-1
When x = 14, y = 2, z = (4*2) – 1 = 7
Now, x varies directly as z = 4y-1
When y = 5, z = (4*5) – 1 = 19
x 14 7
y - 19
Therefore, x = (14*19)/7 = 38
Solution :
Let z = 4y-1
When x = 14, y = 2, z = (4*2) – 1 = 7
Now, x varies directly as z = 4y-1
When y = 5, z = (4*5) – 1 = 19
x 14 7
y - 19
Therefore, x = (14*19)/7 = 38
8) If a flat costs Rs.4500 per sq. ft, and a commercial space costs Rs.9500 per sq. ft, then what is the ratio of their areas if the total cost of both are the same?
a) 9:19b) 19:9
c) 15:28
d) 28:15
ANSWER : 19:9
Solution :
Let A1 be the area of flat and A2 be that of the commercial space
Total cost = area * rate
Therefore, cost of flat = A1*4500 ; cost of commercial space = A2*9500
Both the above costs are same
A1*4500 = A2*9500
A1:A2 = 9500:4500 = 19:9
Solution :
Let A1 be the area of flat and A2 be that of the commercial space
Total cost = area * rate
Therefore, cost of flat = A1*4500 ; cost of commercial space = A2*9500
Both the above costs are same
A1*4500 = A2*9500
A1:A2 = 9500:4500 = 19:9
9) Two natural numbers whose sum is 72 cannot be in the ratio:
a) 1:2b) 3:5
c) 1:3
d) 3:4
ANSWER : 3:4
Solution :
72 should be divisible by addition of the above ratio.
Using trial and error method
For (a): - 1+2 = 3, 72 is divisible by 3
For (b): - 3+5 = 8, 72 is divisible by 8
For (a): - 1+3 = 4, 72 is divisible by 4
For (a): - 3+4 = 7, 72 is not divisible by 7
Therefore, the answer is option (d)
Solution :
72 should be divisible by addition of the above ratio.
Using trial and error method
For (a): - 1+2 = 3, 72 is divisible by 3
For (b): - 3+5 = 8, 72 is divisible by 8
For (a): - 1+3 = 4, 72 is divisible by 4
For (a): - 3+4 = 7, 72 is not divisible by 7
Therefore, the answer is option (d)
10) Two kinds of rice, 1st costs Rs.13 per kg and 2nd costs Rs.19 per kg are mixed together. Find the ratio in which the 2 types are mixed so that the mixture costs Rs.14.2 per kg?
a) 3:1b) 4:1
c) 3:4
d) 4:3
ANSWER : 4:1
Solution :
Let the total quantity of mixture be 1. If quantity of 1st type is x then quantity of the 2nd type will be (1-x)
Therefore, 13x + 19(1-x) = 14.2
13x -19x + 19 = 14.2
4.8 = 6x
x = 0.8 ; (1-x) = 0.2
Therefore, the ratio is 0.8 : 0.2 = 4:1
Solution :
Let the total quantity of mixture be 1. If quantity of 1st type is x then quantity of the 2nd type will be (1-x)
Therefore, 13x + 19(1-x) = 14.2
13x -19x + 19 = 14.2
4.8 = 6x
x = 0.8 ; (1-x) = 0.2
Therefore, the ratio is 0.8 : 0.2 = 4:1
11) The ratio of two numbers is 5:9. If each number is decreased by 5, the ratio becomes 5:11. Find the numbers.
a) 30, 19b) 21, 37
c) 15, 34
d) 15, 27
ANSWER : 15, 27
Solution :
Let the two numbers be 5x and 9x.
(5x-5)/(9x-5) = 5:11
(5x-5)*11 = (9x-5)*5
55x – 55 = 45x – 25
10x = 30
x = 3
Therefore, the numbers are 15 and 27.
Solution :
Let the two numbers be 5x and 9x.
(5x-5)/(9x-5) = 5:11
(5x-5)*11 = (9x-5)*5
55x – 55 = 45x – 25
10x = 30
x = 3
Therefore, the numbers are 15 and 27.
12) In a partnership for a business, Jay invests Rs.6000 for complete year & Viru invests Rs.3000 for 6 months. What is Viru’s share if they earn Rs.240 as profit?
a) 120b) 80
c) 192
d) 48
ANSWER : 48
Solution :
If A invests amount C1 for T1 time and his share of profit is P1, and B invests amount C2 for T2 time and his share of profit is P2, then, C1 * T1 / C2 * T2 = P1/P2
If P is the Viru’s share of profit, then Jay gets (240 – P)
Therefore, 6000 * 12 / 3000 * 6 = (240 - P) / P = 72/ 18 = 4
4P = (240 – P)
5P = 240
P = 48
Solution :
If A invests amount C1 for T1 time and his share of profit is P1, and B invests amount C2 for T2 time and his share of profit is P2, then, C1 * T1 / C2 * T2 = P1/P2
If P is the Viru’s share of profit, then Jay gets (240 – P)
Therefore, 6000 * 12 / 3000 * 6 = (240 - P) / P = 72/ 18 = 4
4P = (240 – P)
5P = 240
P = 48
13) In what ratio should the profit of Rs.8000 be divided if X starts a business with an investment of Rs. 20000, Y invests Rs.7500 for 4 months and Z invests Rs.15000 after 3 months from the start of the business.
a) 16 : 2 : 3b) 8 : 3 : 6
c) 16 : 2 : 9
d) 6 : 9 : 1
ANSWER : 16 : 2 : 9
Solution :
Let the profit of X be P1, that of Y be P2 and of Z be P3.
P1:P2:P3 = 20000*12 : 7500*4 : 15000*9 = 240 : 30 : 135 = 80 : 10 : 45
= 16 : 2 : 9
Solution :
Let the profit of X be P1, that of Y be P2 and of Z be P3.
P1:P2:P3 = 20000*12 : 7500*4 : 15000*9 = 240 : 30 : 135 = 80 : 10 : 45
= 16 : 2 : 9
14) Sanjay, Manoj and Hari rented a field for cattle grazing for Rs.2700. Manoj grazed his 12 cattle for 15 days, Sanjay grazed his 20 cattle for 30 days and Hari grazed his 10 cattle for 12 days. Find out the share that Manoj paid as rent.
a) 1800b) 360
c) 540
d) 900
ANSWER : 540
Solution :
Let the share of Sanjay be X, of Manoj be Y and that of Hari be Z
Therefore, X:Y:Z = 20*30 : 12*15 : 10*12
= 600 : 180 : 120 = 10 : 3 : 2
Now, 10a+3a+2a = 15a = 2700
a = 180
Manoj’s share is Y = 3a = 3*180 = 540
Solution :
Let the share of Sanjay be X, of Manoj be Y and that of Hari be Z
Therefore, X:Y:Z = 20*30 : 12*15 : 10*12
= 600 : 180 : 120 = 10 : 3 : 2
Now, 10a+3a+2a = 15a = 2700
a = 180
Manoj’s share is Y = 3a = 3*180 = 540
15) Sita and Geeta invested Rs.32000 and Rs.24000 respectively for a particular business. After 3 months Sita withdrew Rs.10000 and Geeta invested Rs.10000 more. After another 3 months Radha joins the partnership with an investment of Rs.42000. Find out the amount by which Geeta’s share exceeds from that of Radha’s out of a total profit of Rs.52800 after one year.
a) 3600b) 7200
c) 10800
d) 2400
ANSWER : 7200
Solution :
Let Sita’s share be X, Geeta’s share be Y and Radha’s share be Z.
Sita: - Investment * time = (32000*3) + (22000*9) = 294000
Geeta: - Investment * time = (24000*3) + (34000*9) = 378000
Radha: - Investment * time = (42000*6) = 252000
X:Y:Z = 294000 : 378000 : 252000 = 7 : 9 : 6
X+Y+Z = 52800 = 7a+9a+6a = 22a
a = 2400
Y-Z = 9a – 6a = 3a = 2400*3 = 7200
Solution :
Let Sita’s share be X, Geeta’s share be Y and Radha’s share be Z.
Sita: - Investment * time = (32000*3) + (22000*9) = 294000
Geeta: - Investment * time = (24000*3) + (34000*9) = 378000
Radha: - Investment * time = (42000*6) = 252000
X:Y:Z = 294000 : 378000 : 252000 = 7 : 9 : 6
X+Y+Z = 52800 = 7a+9a+6a = 22a
a = 2400
Y-Z = 9a – 6a = 3a = 2400*3 = 7200
16) Ravi started off with a business with a capital of Rs.60000. Later he was joined by Kishan with Rs.40000 as his share. If Kishan received 1/3rd of the total profit after 1 year, for how many months did he invest?
a) 8b) 4
c) 3
d) 9
ANSWER : 9
Solution :
Let Ravi’s share be X and Kishan’s share be Y.
X : Y = 2 : 1 = 60000*12 : 40000*t ….(where t is number of months Kishan invested his money)
2 : 1 = 72 : 4t
36 = 4t
t = 9
Solution :
Let Ravi’s share be X and Kishan’s share be Y.
X : Y = 2 : 1 = 60000*12 : 40000*t ….(where t is number of months Kishan invested his money)
2 : 1 = 72 : 4t
36 = 4t
t = 9
17) In what ratio should the profit be divided if M, N, O invests capital in ratio 2:3:5 and their timing of their investments are in the ratio 4:5:6.
a) 8:15:30b) 5:18:28
c) 4:5:6
d) 2:3:5
View Answer / Hide Answer
ANSWER : 8:15:30
Solution :
P1:P2:P3 = (2*4):(3*5):(5*6)
= 8 : 15 : 30
Solution :
P1:P2:P3 = (2*4):(3*5):(5*6)
= 8 : 15 : 30
Sample questions on Ratio and Proportion
1. The compounded ratio of (2:3), (6:11) and (11:2) is :
1:22:1
3:1
4:1
2. Divide 1540 chocolate in ramesh, mayur, amit in ratio of 25:15:10.
740, 500, 300770, 462, 308
800, 440, 300
940, 400, 200
3. Zinc and copper are melted together in the ratio 9:11. What is the weight of melted mixture, if 27.9 kg of zinc has been consumed in it?
61 kg62kg
63 kg
64kg
4. If four people L, B, Y, M are getting salary in ratio of 6: 4: 8 : 2 and Y is getting 1500 more than the M, then find out the salary of B?
20001000
1500
1200
5. If a carton containing a dozen mirror is dropped, which of the following cannot be the ratio of broken mirrors to unbroken mirrors?
2:61:2
3:2
2:5
6. If (a+b):(b+c):(c+a)= 2:3:3 and (a+b+c)= 16, then the value of c is:
56
7
8
7. If the salaries of A,B,C are in the ratio of 4:5:6. If the increments of 20%,25% and 30% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
20:21:2225:24:26
24:25:26
26:25:24
8. x varies inversely as square of y. Given that y=2 for x=1. The value of x for y =6 is will be equal to :
1:71:8
8:1
9:1
9. From the salary of an IAS officer, 20% is deducted as house rent, 40% of the rest, he spends on conveyance, 40% of the rest he pays as income tax and 20% of the balance, he spends on clothes. Then, he is left with Rs.32, 000. Find his total salary.
Rs.138,888Rs.130,000
Rs.135,000
Rs.140,000
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