Solution: (c)

Let monthly income of Sneha, Tina and Akruti is 95x, 110x and 116x respectively

Annual income of Sneha = 12 $\displaystyle \times$ 95x = 3,42,000

X = $\displaystyle \frac{{342000}}{{95\times 12}}$

Annual income of Akruti = 12 $\displaystyle \times$ 116x

= $\displaystyle 12\times 116\times \frac{{342000}}{{95\times 12}}$

Akruti’s annual income = ₹ 4,17,600

Alternate method

Irrespective of monthly or annual income, we can solve the question as given below:

Sneha’s Income / Akruti Income = 95/116

342000 / Akruti Income=95/116

Akruti Income= (116 $\displaystyle \times$ 342000)/95 = 417600

Solution: (d)

Ratio of monthly income and ratio of annual income will be the same, ie 84 : 76 : 89

Therefore, Sum of Sita’s and Kunal’s annual income

= $\displaystyle \frac{{456000}}{{76}}\times (84+89)=1038000$

Alternate method

Let monthly income of Sita Riya and Kunal be 84k, 76k and 89k, respectively.
Given annual income of Riya = 456000
Therefore, Monthly income of Riya = 456000/12 = 38000
$\displaystyle \Rightarrow$ 76k = 38000

$\displaystyle \Rightarrow$ k = 500
So, the monthly income of Sita and Kunal = 84k + 89k = 173k
= 173 $\displaystyle \times$ 500 = 86500
Therefore, annual income = 86500 $\displaystyle \times$ 12 = ₹ 1038000

Solution: (b)

$\displaystyle \frac{{x+1}}{{y+2}}=\frac{2}{3}$$\displaystyle \Rightarrow 3x-2y=1$

$\displaystyle \frac{{x+2}}{{y+3}}=\frac{5}{7}$ $\displaystyle \Rightarrow 7x-5y=1$

Or, $\displaystyle 3x-2y=7x-5y$

$\displaystyle \Rightarrow 3y=4x$

$\displaystyle \Rightarrow$$\displaystyle \frac{x}{y}=\frac{3}{4}$

Solution: (e)

According to the question

Present age of Parineeta = 33 – 9 = 24 years

Present age of Manisha = 24 – 9 = 15 years

Present age of Deepali = 24 + 15 = 39 years

Therefore, 5 : X = 15 : 39

$\displaystyle \Rightarrow$x = $\displaystyle \frac{{5\times 39}}{{15}}=13$

Alternate method

Present age of Parineeta is 33 – 9 = 24 years

Age of Manisha = 24 – 9 = 15 years

But from the given information, difference Mamsha and Deepali’s age is 24 years

Deepali’s Age =15+24=39 years

Thus, Deepali’s present age is 39 years.

Now, as the ratio of Manisha’s age and Deepali’s age is , so…

Manisha / Deepali=5 / x

15/39=5/x

15x=95

x=195/15

Therefore, x=13

So, the value of X is 13

Solution: (a)

Let Gloria’s and Sara’s present ages be 4x and 7x years respectively.

Two years ago, $\displaystyle \frac{{4x-2}}{{7x-2}}=\frac{1}{2}$

$\displaystyle \Rightarrow$ 8x – 4 = 7x – 2

$\displaystyle \Rightarrow$ x= 2

Therefore, Sara’s age three years hence = 7x + 3 = 17 years

Alternate method

Let the present age of Gloria and Sara be A and B respectively

It is given that, $\displaystyle \frac{A}{B}=\frac{4}{7}$———–(1)

Two Years back Gloria age will be A – 2 and Sara age will be B – 2 and which is given that

$\displaystyle \frac{{A-2}}{{B-2}}=\frac{1}{2}$————(2)

Solving the two equations we get B=14 years, so three years hence age of Sara will be=14+3=17 years