17. Rs.5625 is divided among A, B and C so that A may receive $\displaystyle\frac{1}{2}$ as much as B and C together receive, B receives $\displaystyle\frac{1}{4}$ of what A and C together receive. The share of A is more than that of B by :
a. Rs.750
b. Rs.775
c. Rs.1500
d. Rs.1600

Answer: A

Explanation:
A=$\displaystyle\frac{1}{2}$ (B + C) or B + C = 2A
$ \Rightarrow $ A + B + C = 3A
Thus , 3A = 5625 or A =1875
Again, B = $\displaystyle\frac{1}{4}$ (A+C)$ \Rightarrow $ A+C=4B
$ \Rightarrow $A + B+ C = 5B
5B=5625 or B = 1125
Then, A's share is more than that of B by
Rs.(1875 - 1125) i.e. Rs.750

18. A certain amount was divided between Kavita and Reena in the ratio of 4:3. If Reena's share was Rs.2400, the amount is :
a. Rs. 5600
b. Rs. 3200
c. Rs. 9600
d. Rs. 9800

Answer: A

Explanation:
Let their shares be Rs.4x and Rs.3x.
Thus, 3x = 2400 $ \Rightarrow $ x = 800
Total amount = 7x = Rs.5600

19. The prices of a scooter and a television set are in the ratio 3:2 . If a scooter costs Rs.6000 more than the television set, the price of the television set is :
a. Rs.6000
b. Rs.10,000
c. Rs.12,000
d. Rs.18,000

Answer: C

Explanation:
Let the price of scooter be Rs.3x and that of a television set be Rs.2x.
Then 3x - 2x = 6000 or x = 6000
Cost of a television set = 2x = Rs.12000

20. If 18:x = x:8, then x is equal to :
a. 144
c. 72
c. 26
d. 12

Answer: D

Explanation:
$18 \times 8 = {x^2}$ or x = $\sqrt {144} = 12$

21. A right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is :
a. 3:5
b. 2:5
c. 3:1
d. 1:3

Answer: D

Explanation:
Let the heights of the cylinder and cone be h and H respectively. Then,
$\pi {r^2}h = \displaystyle\frac{1}{3}\pi {r^2}H$ or $\displaystyle\frac{h}{H} = \displaystyle\frac{1}{3}$
So, their heights are in the ratio 1 : 3

22. A circle and square have same area. Therefore, the ratio of the side of the square and the radius of the circle is :
a. $\sqrt \pi :1$
b. $1:\sqrt \pi $
c. $1:\pi $
d. $\pi :1$

Answer: A

Explanation:
Let the side of the square be x and let the radius of the circle be y.
Then, ${x^2} = \pi {y^2} \Rightarrow \displaystyle\frac{{{x^2}}}{{{y^2}}}\pi $ or $\displaystyle\frac{x}{y} = \sqrt \pi $
x : y = $\sqrt \pi :1$

23. In a class, the number of boys is more than the number of girls by 12% of the total strength. The ratio of boys to girls is :
a. 11:4
b. 14:11
c. 25:28
d. 28:25

Answer: B

Explanation:
Let the number of boys and girls be x and y respectively. Then (x-y) = 12% of (x+y)
or x - y = $\displaystyle\frac{3}{{25}}$ (x+y)
25x - 25y=3x + 3y or 22x = 28y
or $\displaystyle\frac{x}{y} = \displaystyle\frac{{28}}{{22}} = \displaystyle\frac{{14}}{{11}} = 14:11$

24. A, B and C do a work in 20, 25 and 30 days respectively. They undertook to finish the work together for Rs.2220, then the share of A exceeds that of B by :
a. Rs.120
b. Rs.180
c. Rs.300
d. Rs.600

Answer: B

Explanation:
Remember remuneration is inversely proportional to the days taken to complete the work.
Ratio of shares of A,B & C = $\dfrac{1}{{20}}:\dfrac{1}{{25}}:\dfrac{1}{{30}} = \dfrac{{15:12:10}}{{300}}$ ($\because $ by taking LCM of 20, 25, 30 and multiplying the given ratios)
Sum of the ratios = 15 + 12 + 10 = 37.
A's share = Rs.$\left( {2220 \times \displaystyle\frac{{15}}{{37}}} \right) = Rs.900$
B's share = Rs.$\left( {2220 \times \displaystyle\frac{{12}}{{37}}} \right) = Rs.720$
Thus, the share of A exceeds that of B by Rs.
(900 - 720) = Rs.180