if a:b = c:d then (a+b)/(a-b) = (c+d)/(c-d) |
x ∝ y then x =
k*y where k = constant |
x ∝ 1/ y then x * y= k where k = constant |
Q. If a:b = 3:4 and b:c is 5:4 then find a:b:c
A. The value common to both is b so b has to made same in both ratios. The LCM of 4,5 is 20 so we convert the ratios by multiplication
a:b = (3*5):(4*5) and b:c = (5*4)/(4*4)
a:b = 15:20 and b:c = 20:16 now b value is same in both sides and so we can merge on basis of 'b'.
a:b:c = 15:20:16
Q.Find fourth proportional between 4,9,12
A. Assume fourth proportional as 'x'. so we get 4:9::12:x .
As we know from above formula: 4*x = 9*12 so we can get value of x.
Q. Third proportional to 16, 36.
A. Assume third proportional is 'x'. so we get 16:36::36:x
As we know from formula that 16*x = 36*36 we can get 'x'.
Q. Mean proportional between 0.08 and 0.18
A. mean proportional = square-root(0.08*0.18)
= square-root(8/100 * 18/100)
= square-root(144/10000)
=12/100
=0.12
Q. If x : y = 3 : 4, find (4x + 5y) : (5x - 2y)
A. 4x+5y : 5x-2y = 4(x/y)+5 / 5(x/y) - 2 we get this by dividing by y to both numerator and denominator.
substituting x/y in equation we can solve it.
Q. Divide Rs. 600 in the ratio 4:2
A. the ratio 4:2 means first value shall be 4/4+2 and second value shall be 2/4+2 i.e. 600 has to be divided into 4/6 and 2/6 parts. so we get 400,200.
Q. A bag contains 50 p, 25 P and 10 p coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of coins of each type.
A. Since ratio is 5:9:4 this means actual number of coins can be 5x, 9x and 4x.
We know that, 5x*(1/2) + 9x*(1/4) + 4x*(1/10) = 206 as we converted the paisa values to rupee.
Q. A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.
A. Alcohol and water were 4x and 3x and
now 4x / 3x+5 = 4 / 5.
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