Ratio and Proportion Questions - 1

If a sum of Rs.17,100 is divided between, A and B in the ratio 4:5, how much amount would A get ?
  • Rs. 9500
  • Rs. 6700
  • Rs. 7600
  • Rs. 7900
  • Rs. 9700
Explanation   

A = 17100 $\displaystyle \times \frac{4}{9}$ = Rs.7600.

B = 17100 $\displaystyle \times \frac{5}{9}$ = Rs.9500.

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If an amount of Rs.16,900 is divided among A, B and C in the ratio $\displaystyle \frac{1}{4} : \frac{1}{3} : \frac{1}{2}$, what will be the amount received by C ?
  • Rs.7800
  • Rs.7900
  • Rs.8450
  • Rs.8500
  • Rs.9200
Explanation   

A : B : C = $\displaystyle \frac{1}{4} : \frac{1}{3} : \frac{1}{2} = \frac{3 : 4 : 6}{12}$

Actual ratio of A : B : C = 3 : 4 : 6.

C = 16900 $\displaystyle \times \frac{6}{13}$ = Rs.7800.

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If an amount of Rs.55500, is to be divided among X, Y and Z in the ratio $\displaystyle \frac{1}{4} : \frac{1}{5} : \frac{1}{6}$, then what is the difference between the amount received by X and Y ?
  • Rs.3000
  • Rs.3700
  • Rs.6100
  • Rs.1800
  • Rs.4500
Explanation   

X : Y : Z = $\displaystyle \frac{1}{4} : \frac{1}{5} : \frac{1}{6} = \frac{15:12:10}{60}$

Actual ratio of X : Y : Z = 15 : 12 : 10.

X = 55500 $\displaystyle \times \frac{15}{37}$ = 22500.

Y = 55500 $\displaystyle \times \frac{12}{37}$ = 18000.

X – Y = Rs.22500 – Rs.18000 = Rs.4500.

OR

Difference in ratio of X and Y = 15 – 12 = 3.

X – Y = 55500 $\displaystyle \times \frac{3}{37}$ = Rs.4500.

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In a bag there are 50np, 25np and 10np coins in the ratio 5 : 6 : 7, amounting to Rs.235. Find the number of 50np coins in the bag ?
  • 240
  • 470
  • 250
  • 325
  • 235
Explanation   

Value of the coins:

50 np = $\displaystyle \frac{50}{100} = \frac{1}{2} \times 5 = \frac{5}{2}$

25 np = $\displaystyle \frac{25}{100} = \frac{1}{4} \times 6 = \frac{6}{4}$ or $\displaystyle \frac{3}{2}$

10 np = $\displaystyle \frac{10}{100} = \frac{1}{10} \times 7 = \frac{7}{10}$

Ratio of the value of the coins = $\displaystyle \frac{5}{2} : \frac{3}{2} : \frac{7}{10} = \frac{25 : 15 : 7}{10}$

Therefore the value of 50np, 25np, 10np is in the ratio = 25 : 15 : 7.

Value of 50np = 235 $\displaystyle \times \frac{25}{47}$ = 5 x 25 = Rs.125 => number of coins = 125 x 2 = 250 coins.

25np = 235 $\displaystyle \times \frac{15}{47}$ = 5 x 15 = Rs.75 => number of coins = 75 x 4 = 300 coins.

10np = 235 $\displaystyle \times \frac{7}{47}$ = 5 x 7 = Rs.35 => number of coins = 35 x 10 = 350 coins.

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In a bag there are Rs.2, 50np and 20np coins, in the ratio 3 : 4 : 7. If the number of 20np coins is 420, then what is the total amount in the bag ?
  • Rs.465
  • Rs.654
  • Rs.564
  • Rs.450
  • Rs.582
Explanation   

Value of the coins:

Rs.2 = $\displaystyle \frac{200}{100} = \frac{2}{1} \times 3$ = 6.

50np = $\displaystyle \frac{50}{100} = \frac{1}{2} \times 4$ = 2.

20np = $\displaystyle \frac{20}{100} = \frac{1}{5} \times 7 = \frac{7}{5}$

Ratio of the value of the coins = 6 : 2 : $\displaystyle \frac{7}{5} = \frac{30 : 10 : 7}{5}$

Therefore the value of the coins = 30 : 10 : 7.

As value of 20np coins = $\displaystyle \frac{420}{5}$ = Rs.84.

Total value of the coins = $\displaystyle \frac{84}{7} \times 47$ = Rs.564.

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An amount is divided among X, Y and Z in the ratio 3 : 4 : 5. The difference between the amount received by X and Z is Rs.1842. What is the total amount which was divided in the beginning ?
  • Rs.11,052
  • Rs.18,420
  • Rs.9,210
  • Rs.6,864
  • Rs.6,464
Explanation   

Let X, Y and Z be 3x : 4x : 5x.

X – Z = 3x – 5x = 2x = 1842 => x = $\displaystyle \frac{1842}{2}$ = 921.

Total X + Y + Z = 3x + 4x + 5x = 12x = 12 X 921 = Rs.11,052.

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In a container there are two solutions; solution A and solution B in the ratio of 3 : 4. If 8 litres of solution A is added, the ratio becomes 11:12. What is the total quantity in the container after adding the extra 8 litres ?
  • 96 liters
  • 104 liters
  • 94 liters
  • 92 liters
  • 112 liters
Explanation   

Let Solution A : Solution B be = 3x : 4x.

$\displaystyle \frac{\text{Solution A}}{\text{Solution B}} = \frac{3\text{x} \ + 8}{4\text{x}} = \frac{11}{12}$

36x + 96 = 44x => 8x = 96 => x = 12.

Solution A + Solution B = 3x + 8 + 4x = 32 + 8 + 48 = 92 liters.

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Age of a father and his son is in the ratio of 5 : 2. After two years, the ratio becomes 19 : 8. What are the present ages of father and son respectively ?
  • 45 and 12
  • 35 and 12
  • 55 and 22
  • 40 and 16
  • 45 and 18
Explanation   

Let present ages of father and son be 5x : 2x.

After two years: $\displaystyle \frac{5\text{x} \ + 2}{2\text{x} \ + 2} = \frac{19}{8}$

40x + 16 = 38x + 38 => 2x = 22 => x = 11.

Father = 5x = 5 x 11 = 55; Son = 2x = 2 x 11 = 22.

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Age of a father and his son 4 years ago was in the ratio 7:1. After 4 years, the ratio of ages will be in 3:1. What are the present ages of father and son ?
  • 40 and 10
  • 28 and 4
  • 32 and 8
  • 45 and 9
  • 35 and 5
Explanation   

4 years ago (-)Present + 4 hence = ( 8 years from 4years ago ).

Four years ago means 4 years less then present age,

After 4 years means 4 years more than present age.

Here you can calculate from 4 years ago, i.e with ratio 7:1, and adding 8 [8 years] to the past Given ratio of ages.

Let age of Father and son 4 years ago was = 7x : x

After 4 years from present age = $\displaystyle \frac{7\text{x} \ + 8}{\text{x} \ + 8} = \frac{3}{1}$

=> 7x + 8 = 3x + 24 => 4x = 16 or x = 4 or 4 years.

Father’s age 4 years ago was 7 x 4 = 28, Son age 4 years ago was x = 4 years.

Present ages of Father and son = 28 + 4 = 32 years; son = 4 + 4 = 8 years.

For example in case your present age is not mentioned, but your age 4 years ago was 28, your age after 4 years from now will be 28 + 8 = 36 years, present = 28 + 4 or 36 - 4 = 32 years.

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Ratio of salary of Rekha and Sudha is 6:7 respectively. Their expenditure is in the ratio of 1:1 and their savings are in the ratio 1:2 respectively. Together, they save Rs.12,000. What is the income of Sudha ?
  • Rs.30,000
  • Rs. 32,000
  • Rs. 24,000
  • Rs.33,000
  • Rs. 28,000
Explanation   

Income – Savings = Expenditure.

Let income of Rekha and Sudha be 6x : 7x respectively.

Savings Rekha = 12000 $\displaystyle \times \frac{1}{3}$ = Rs.4000.

Savings Sudha = 12000 $\displaystyle \times \frac{2}{3}$ = Rs.8000.

$\displaystyle \frac{\text{Rekha}}{\text{Sudha}} = \frac{6\text{x} \ - 4000}{7\text{x} \ - 8000} = \frac{1}{1}$

=> 6x – 4000 = 7x – 8000 = x = Rs.4000.

Income of Rekha = 6x = 6 x 4000 = Rs.24,000; Sudha = 7x = 7 x 4000 = Rs.28,000.

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