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# Arithmetic Aptitude :: Ratio & Proportion

Home > Arithmetic Aptitude > Ratio & Proportion > General Questions

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1. 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?

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Explanation:

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.

Then 4x - 3x = 1000

x = 1000.

So B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.

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2. 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:

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Explanation:

Let the three parts be A, B, C. Then,

A : B = 2 : 3 and B : C = 5 : 8 = 5 * 3/5 : 8 * 3/5 = 3 : 24/5

=> A : B : C = 2 : 3 : 24/5 = 10 : 15 : 24

=> B = 98 x 15/49 = 30.

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3. Three sales people are paid commissions in proportion to the amount of their sales, which total \$25000, \$40000, and \$60000 respectively. If a total of \$20000 is allocated for these three commissions, what is the amount of the largest commission paid?

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Explanation:

The proportion of their commission = 25000:40000:60000
=> 5:8:12
So the largest commission =(12/25)*20000 = \$9600.

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4. Two boys begin together to write out a booklet containing 535 lines. The first boy starts with the first line, writing at the rate of 100 lines an hour; and the second starts with the last line then writes line 534 and so on, backward proceeding at the rate of 50 lines an hour. At what line will they meet?

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Explanation:

Writing ratio = 100:50= 2:1
Since equal quantities are taken,
Therefore in a given time, first boy will be writing the line number
2/3 * 535
=> 356 2/3 or 357th line.
Hence, both of them shall meet on 357th line.

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5. Three men rent a farm for Rs. 7000 per annum. A puts 110 cows in the farm for 3 months, B puts 110 cows for 6 months and C puts 440 cows for 3 months. What percentage of the total expenditure should A pay?

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Explanation:

A:B:C=110*3:110*6:440*3 = 3:6:12 = 1:2:4

share of A = 1/(1+2+4) * 7000 = 1000

% expenditure of A = 1000/7000 *100 = 100/7 = 14.28%

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6. In a mixture of a, b, & c, if a and b are mixed in 3:5 ratio and b and c are mixed in 8:5 Ratio and if the final mixture is 35 liters, find the amount of b?

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Explanation:

The ratio is A:B:C =24:40:25
So, B=35*40/89=15.73

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7. Ten years ago A was half of B's Age. If ratio of their present ages is 3:4 then what is the total of their present ages?

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Explanation:

Lets say ten years ago A was half of B's age so,take 5 : 10
Now,after 10 years A is 15 and B is 20
15:20 is 3:4 so,combined age is 15+20 = 35

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8. If A and B get profits of Rs. 6000 and Rs. 4000 respectively at the end of year the ratio of their investments are

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Explanation:

profit=Investment * Time
so, 6000=invest-1 *1=6000
4000=invest-2 * 1= 4000
invest-1/inverst-2=6000/4000=3/2

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9. If shares of two persons in profits are Rs.400 and Rs.600 then ratio of their capitals is

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Explanation:

Total Profit= Rs. 1000
Ratio=400/600=2:3

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10. If the ratio of ages of two friends is 4:3 and sum of their ages is 70 years then what is the age of older friend?

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