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41. Number of students in institutes A and B were in the ratio of 7 : 15 respectively in 2012. In 2013, the number of students in institute A increased by 25% and number of students in institutes B increased by 26%, then what was the respective ratio between number of students in institutes A and B?

A. 25 : 56

B. 24 : 55

C. 24 : 53

D. 25 : 53

Discuss

Solution:

Ratio of students in 2012 in institutes A and B = 7 : 15
Let number of students in institute A in 2012 = 700
And Number of students in institutes B in 2012 = 1500
25% increase in the number of students in 2013
Now, number of students in Institute A = 700 + 25% of 700 = 875
Number of students in B in 2013 as 26% students increased in B
= 1500 + 26% of 1500 = 1890
Current Ratio of the students,

= \frac{875}{1890} = 25 : 54

42. A and B together have Rs. 1210. If $\frac{4}{15}$ of A's amount is equal to $\frac{2}{5}$ of B's amount, how much amount does B have?

A. Rs. 460

B. Rs. 484

C. Rs. 550

D. Rs. 664

Discuss

Solution:

\begin{aligned} \frac{4}{15} A = \frac{2}{5} B \\ \Rightarrow A = (\frac{2}{5} \times \frac{15}{4}) B \\ \Rightarrow A = \frac{3}{2} B \\ \Rightarrow \frac{A}{B} = \frac{3}{2} \\ \Rightarrow A : B = 3 : 2. \\ ∴ B's share = R s . (1210 \times \frac{2}{5}) \\ = R s . 484 \end{aligned}

43. Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

A. 2 : 5

B. 3 : 5

C. 4 : 5

D. 6 : 7

Discuss

Solution:

\begin{aligned} Let the third number be x \\ Then, first number \\ = 120 % of x = \frac{120 x}{100} = \frac{6 x}{5} \\ Second number \\ = 150 % of x = \frac{150 x}{100} = \frac{3 x}{2} \\ ∴ Ratio of first two numbers \\ = \frac{6 x}{5} : \frac{3 x}{2} = 12 x : 15 x = 4 : 5 \end{aligned}

44. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?

A. Rs. 500

B. Rs. 1500

C. Rs. 2000

D. None of these

Discuss

Solution:

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively
Then, 4x - 3x = 1000
⇒ x = 1000
∴ B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000

45. Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

A. 2 : 3 : 4

B. 6 : 7 : 8

C. 6 : 8 : 9

D. None of these

Discuss

Solution:

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x)

= (\frac{140}{100} \times 5 x),

(\frac{150}{100} \times 7 x)

and

(\frac{175}{100} \times 8 x)

\begin{aligned} = 7 x, \frac{21 x}{2} and 14 x \\ ∴ The required ratio \\ = 7 x : \frac{21 x}{2} : 14 x \\ = 14 x : 21 x : 28 x \\ = 2 : 3 : 4 \end{aligned}

46. In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quanity of water to be further added is:

A. 20 litres

B. 30 litres

C. 40 litres

D. 60 litres

Discuss

Solution:

Quantity of milk

= (60 \times \frac{2}{3}) litres = 40 litres

Quantity of water in it = (60 - 40) litres = 20 litres
New ratio = 1 : 2
Let quantity of water to be added further be x litres

\begin{aligned} Then, milk : water = \frac{40}{20 + x} \\ Now, \frac{40}{20 + x} = \frac{1}{2} \\ \Rightarrow 20 + x = 80 \\ \Rightarrow x = 60 \\ ∴ Quantity of water to be added = 60 litres . \end{aligned}

47. The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio?

A. 8 : 9

B. 17 : 18

C. 21 : 22

D. Cannot be determined

Discuss

Solution:

Originally, let the number of boys and girls in the college be 7x and 8x respectively
Their increased number is (120% of 7x) and (110% of 8x)

\begin{aligned} \Rightarrow (\frac{120}{100} \times 7 x) and (\frac{110}{100} \times 8 x) \\ \Rightarrow \frac{42 x}{5} and \frac{44 x}{5} \\ ∴ The required ration \\ = \frac{42 x}{5} : \frac{44 x}{5} \\ = 21 : 22 \end{aligned}

48. Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary?

A. Rs. 17,000

B. Rs. 20,000

C. Rs. 25,500

D. Rs. 38,000

Discuss

Solution:

Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively

Then, \frac{2 x + 4000}{3 x + 4000} = \frac{40}{57}

⇒ 57(2x + 4000) = 40(3x + 4000)
⇒ 6x = 68,000
⇒ 3x = 34,000
Sumit's present salary
= (3x + 4000)
= Rs. (34000 + 4000)
= Rs. 38,000

49. If 0.75 : x :: 5 : 8, then x is equal to:

A. 1.12

B. 1.2

C. 1.25

D. 1.30

Discuss

Solution:

\begin{aligned} x \times 5 = 0.75 \times 8 \\ \Rightarrow x = \frac{6}{5} \\ \Rightarrow x = 1.2 \end{aligned}

50. The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:

A. 20

B. 30

C. 48

D. 58

Discuss

Solution:

Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8

\begin{aligned} = (5 \times \frac{3}{5}) : (8 \times \frac{3}{5}) = 3 : \frac{24}{5} \\ \Rightarrow A : B : C = 2 : 3 : \frac{24}{5} = 10 : 15 : 24 \\ \Rightarrow B = 98 \times \frac{15}{49} = 30 \end{aligned}

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