The ratio of the volumes of two cubes is 1 : 27. The ratio of their surface areas will be

Solution
Let the edges of the cubes be x and y units respectively.
∴ \(\frac{x^{3}}{y^{3}} = \frac{1}{27}\)
⇒ \(\frac{x}{y} = \sqrt[3]{\frac{1}{27}} = \frac{1}{3}\)
∴ \(\frac{S_{1}}{S_{2}} = \frac{6x^{2}}{6y^{2}}\)
= \(\left (\frac{x}{y} \right )^{2} = \left (\frac{1}{3} \right )^{2} = \frac{1}{9}\)
The population of a town increases at 10% per annum. If the present population is 160000, what will be the population after 4 years?

Solution
Required population
= \(160000\left ( 1 + \frac{5}{100} \right )^{4}\)
= \(160000\left (\frac{21}{20} \right )^{4}\)
= \(\frac{160000 \times 21 \times 21 \times 21 \times 21}{20 \times 20 \times 20 \times 20}\)
= 1,94,481
The sum of two numbers is 100 and their difference is 50. The ratio of these numbers is

Solution
Let the numbers be x and y and x > y.
∴ x + y = 100 ...........(i)
x  Y = 50 ..............(ii)
On adding,
2x = 150 ⇒ x = ^{150}⁄_{2} = 75
From equation (i),
75 + Y = 100
⇒ Y = 100  75 = 25
∴ x : y = 75 : 25 = 3 : 1
A sum doubles in 20 years at a certain rate of simple interest. In how many years will it be four times of itself ?

Solution
Case I
Let, principal be Rs. x.
∴ S.I. = Rs. x
∴ \(x = \frac{x \times 20 \times R}{100} \Rightarrow R = 5\)
Case II
S.I. = 4x  x = Rs.3x
∴ \(3x = \frac{x \times T \times 5}{100}\)
⇒ \(T = \frac{3 \times 100}{5} = 60\) years
The number whose 20% is 10, is

Solution
Let the number be x.
According to the question.
20 % of x = 10
⇒ x × ^{20}⁄_{100} = 10
⇒ ^{x}⁄_{5} = 10
⇒ x = 5 × 10 = 50
To get 35% of a number, the number should be multiplied by

Solution
35% = ^{35}⁄_{100} = ^{7}⁄_{20}
Raman’s salary is decreased by 10%. By what per cent his decreased salary be raised to have the original salary?

Solution
Let the original salary be Rs.100.
New salary = Rs. 90
∴ Increase on Rs. 90
= Rs. 10
∴ Increase on Rs. 100
= \(\frac{10}{90} \times 100 = \frac{100}{9} = 11\frac{1}{9}\%\).
36% of 4800 × 0.2% of 1320 = ?

Solution
? = \(4800 \times \frac{36}{100} \times \frac{1320 \times 0.2}{100}\)
= 1728 × 2.64
= 4561.92
741560 + 935416 + 1143 + 17364 = ?

Solution
? = 741560 + 935416 + 1143 + 17364 = 1695483
(7857 + 3596 + 4123) ÷ 96 = ?

Solution
? = (7857 + 3596 + 4123) ÷ 96
= \(\frac{15576}{96} = \frac{649}{4} = 162.25\).