BANK & INSURANCE (RATIO AND PROPORTION) PART 1

Let the share of Abhishek and Pritha are 5x and 7x.

Given that, 5x + 2000 = 7x

⇒ 2x = 2000

⇒ x = 1000

∴ Abhishek’s share = 5x = 5000

Two numbers are in the ratio of 21 : 26. If 8 is added in each, the new numbers are in the ratio of 5 : 6.

Let the numbers be 21x and 26x.

(21x + 8) / (26x + 8) = 5/6

⇒ 6(21x + 8) = 5(26x + 8)

⇒ 126x + 48 = 130x + 40

⇒ x = 2

⇒ So, the numbers will be 42 and 52.

⇒ If 4 is subtracted, the numbers will be 38 and 48.

∴ Required ratio = 38 : 48 i.e. 19 : 24

∴ The required answer is 19 : 24

The ratio of two numbers = 2 : 3

Let the number be 2x and 3x

(2x + 4) / (3x + 4) = 5/7

⇒ 14x + 28 = 15x + 20
⇒ x = 8
Difference in the numbers = 3x − 2x = x = 8
∴ The difference in the numbers is 8

Income ratio = 3 : 5 : 12
Expenditure ratio = 1 : 2 : 6
C's savings = 1/4 of income

Let the incomes be 3x, 5x, 12x
and expenditure be y, 2y, 6y

A.T.Q (Acc to Ques)

12x − 6y = 1/4 × 12x

⇒ 9x = 6y

⇒ x : y = 2 : 3

Income = 6 ratio, 10 ratio, 24 ratio
Expenditure = 3 ratio, 6 ratio, 18 ratio

Savings = (6 − 3) : (10 − 6) : (24 − 18)

⇒ 3 : 4 : 6

∴ The answer is 3 : 4 : 6

Rohit and Ravi ratio of their Savings = 3 : 2

Combined saving of Rohit and Ravi is Rs. 5000

Rohit Saving = 3000
Ravi Saving = 2000

Income − Savings = Expenditure

According to question,

(5x − 3000)/(4x − 2000) = 6/5

on solving we get, x = 3000

Monthly earning of Rohit = 5 × 3000 ⇒ 15000

∴ Half Yearly earning of Rohit = 6 × 15000 ⇒ 90000

The expenditure of two roommates is in the ratio 3 : 4.

If each spends Rs. 6000 less, the ratio becomes 5 : 8.

Let their initial expenditures be 3x and 4x

After curtailing the expenditures, their expenditures would be (3x − 6000) & (4x − 6000) respectively.

New ratio =

(3x − 6000)/(4x − 6000) = 5/8

⇒ 24x − 48000 = 20x − 30000

⇒ x = 4500

∴ Initial expenditures are Rs. 13500 and Rs. 18000 respectively.

∴ Difference of expenditures = Rs. 4500

A invest 80% of his income on mutual fund, real estate and insurance in the ratio of 3 : 5 : 7 respectively.

Let the income of A be Rs. 'x', then investment

= 0.8x and saving = 0.2x

⇒ 3/15 × 0.8x = 24000

⇒ x = 24000 × 5/0.8

⇒ x = Rs.1,50,000

∴ saving = 0.2x = 1,50,000 × 0.2 = Rs. 30,000

Income = 9 : 11
Expenditure = 5 : 7
savings = Rs. 4400

Let the income of A be Rs. 9x
Income of B = Rs. 11x

Expenditure of A = 5y
Expenditure of B = 7y

So, 9x − 5y = 4400 .........(1)
11x − 7y = 4400 ..........(2)

(1) × 7 − (2) × 5 gives,

63x − 35y − 55x + 35y = 8800

⇒ 8x = 8800

⇒ x = Rs. 1100

∴ Difference = 2x = Rs. 2200

∴ The answer is Rs. 2200

Let savings of A and B be Rs.3n and Rs.4n respectively.

4n − 3n = 2000

⇒ n = 2000

The savings of A = 2000 × 3 = Rs.6000

The savings of B = 2000 × 4 = Rs.8000

Total savings of A and B = 6000 + 8000 = Rs.14000

Required average = 14000/2 = Rs.7000

Therefore the correct answer is Rs.7000

According to question,

Expenditure = Income − Saving

⇒ 9/5 = (5x − 1300)/(3x − 900)

⇒ 9 (3x − 900) = (5x − 1300) × 5

⇒ 2x = 1600

⇒ x = 800

∴ Difference between their monthly income

(5x − 3x) = 2x

⇒ Difference between their monthly income

= 2 × (800) = Rs. 1600

⇒ Difference between their yearly income

= 12 × (1600) = Rs. 19200

∴ The difference between their yearly Incomes is Rs. 19200.