If \(Rs. 782\) be divided into three parts, proportional to \(\frac{1}{2} : \frac{2}{3} : \frac{3}{4}, \) then the first part is:
Answer: D
Given ratio \(= \frac{1}{2} :\frac{2}{3} : \frac{3}{4} = 6:8:9\)
\(\therefore \) 1st part \(= Rs. (782 \times \frac{6}{23}) = Rs. 204\)
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A sum of money is to be distributed among \(A, B, C, D\) in the proportion of \(5 : 2 : 4 : 3.\) If \(C\) gets \(Rs. 1000\) more than \(D,\) what is \(B's\) share?
Answer: A
Let the shares of \(A, B, C\) and \(D\) be \(RS. 5x, Rs. 2x, Rs. 4x\) and \(Rs. 3x\) respectively.
Then, \(4x - 3x = 1000\)
\(\Rightarrow x = 1000.\)
\(\therefore B's\) share \(= Rs. 2x = Rs. (2 \times 1000) = Rs. 2000.\)
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The salaries \(A, B, C\) are in the ratio \(2 : 3 : 5.\) If the increments of \(15\)%, \(10\)% and \(20\)% are allowed respectively in their salaries, then what will be new ratio of their salaries?
Answer: C
Let \(A = 2k, B = 3k\) and \(C = 5k.\)
\(A's\) new salary \(= \frac{115}{100}\) of \(2k = (\frac{115}{100} \times 2k) = \frac{23k}{10}\)
\(B's\) new salary \(= \frac{110}{100}\) of \(3k = (\frac{110}{100} \times 3k) = \frac{33k}{10}\)
\(C's\) new salary \(= \frac{120}{100}\) of \(5k = (\frac{120}{100} \times 5k) = 6k\)
\(\therefore\) New ratio \((\frac{23k}{10} : \frac{33k}{10} : 6k) = 23 : 33 : 60\)
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Salaries of Piu and Amit are in the ratio \(2 : 3.\) If the salary of each is increased by \(Rs. 4000,\) the new ratio becomes \(40 : 57.\) What is Amit's salary?
Answer: A
Let the original salaries of Piu and Amit be \(Rs. 2x\) and \(Rs. 3x\) respectively.
Then, \(\frac{2x + 4000}{3x + 4000} = \frac{40}{57}\)
\(\Rightarrow 57(2x + 4000) = 40(3x + 4000)\)
\(\Rightarrow 6x = 68,000\)
\(\Rightarrow 3x = 34,000\)
Amit's presents salary \(= (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000.\)
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The sum of three numbers is \(98.\) If the ratio of the first to second is \(2 :3\) and that of the second to the third is \(5 : 8,\) then the second number is:
Answer: B
Let the three part be \(A, B, C.\)
Then, \(A:B = 2:3\) and \(B:C = 5:8 = (5 \times \frac{3}{5}):(8 \times \frac{3}{5}) = 3:\frac{24}{5}\)
\(\Rightarrow A:B:C = 2:3:\frac{24}{5} =10:15:24\)
\(\Rightarrow B = (98 \times \frac{15}{49}) = 30.\)
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