If A and B are in the ratio of 4 : 5 and the difference of their squares is 81. What is the value of A ?
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Solution
Let the numbers are 4x & 5x
∴ (5x)2 – (4x)2 = 81
x = 3
∴ A = 4 × 3 = 12
The least number which when divided by 6, 9, 12, 15, 18 leaves the same remainder 2 in each case is :
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Solution
Number = LCM of (6, 9, 12, 15 & 18) + 2
= 182
If the measure of three angles of a triangle are in the ratio 2 : 3 : 5, then the triangle is :
If then the value of is :
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Solution
(Cubing both sides)
Two pipes can separately fill a tank in 20 hrs and 30 hrs respectively. Both the pipes are opened to fill the tank but when the tank is 1/3 rd full a leak develops in the tank through which 1/3 rd of the water supplied by both the pipes leak out. What is the total time taken to fill the tank?
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Solution
Time taken to fill the tank =
∴ 1/3 rd of tank is filled in
Now the pipes are only as efficient as earlier
∴ The work of 8 hours will be completed now in
∴ Total time = 12 + 4 = 16 hrs.
An amount of money grows upto Rs 4840 in 2 years and upto Rs 5324 in 3 years on compound interest. Find the rate percent :
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Solution
Rate =
In a class there are 20 boys whose average is decreased by 2 months, when one boy aged 18 years is replaced by a new boy. Find the age of the new boy :
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Solution
Age of new boy =
= 14 years 8 months
A solution of salt and water contains 15% salt by weight of it, 30 kg water evaporates and the solution now contains 20% of salt. Find the original quantity of salt :
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Solution
Let the solution is x kg.
∴ Salt =
After evaporation
20% of (x – 30) =
⇒ x = 120 kg
∴ Quantity of salt =
A man loses 20% of his money and after spending 70% of the remainder, he is left with Rs. 120. How much had he at first?
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Solution
120 = 24%
∴
Two numbers are respectively 20% and 25% of a third number. What percentage is the first of the second ?
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Solution
Let the third number is 100
∴ Required percentage =