A = 17100 $\displaystyle \times \frac{4}{9}$ = Rs.7600.
B = 17100 $\displaystyle \times \frac{5}{9}$ = Rs.9500.
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.
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.
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.
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.
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.
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.
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.
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.
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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