17
Q:

How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per Kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per Kg ?

 A) 36 Kg B) 42 Kg C) 54 Kg D) 63 Kg

Answer:   D) 63 Kg

Explanation:

By the rule of alligation:
C.P. of 1 kg sugar of 1st kind      C.P. of 1 kg sugar of 2nd kind

${\color{Blue}&space;\therefore&space;}$ Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.

Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg.

Q:

A Container has a capacity of 48 litres and is full of milk. 4 liters of milk is taken out of it and replaced by same quantity of water. Again 4 liters of the mixture is taken out and replaced by the same quantity of water . The process is repeated five times. How much milk is left in the mixture ?

Answer

$\inline \dpi{100} \fn_cm \frac{Milk\: Left\: in\: the\: container\: after\: the\: operations}{Original\: quantity\: of\: milk\: in\: the\: container\: }$ = $\inline \dpi{100} \fn_cm (\frac{Total\: quantity\: of\: milk - quantity\: drawn\: each\: time}{Total\: mixture })^n$

$\inline \dpi{100} \fn_cm \frac{Milk\: left\: in\: the\: container}{48 }=[\frac{48-4}{5}]^5$

Milk left in the container = $\inline \dpi{100} \fn_cm [\frac{44}{48}]^5\times 48$

$\inline \dpi{100} \fn_cm \frac{11}{12}\times \frac{11}{12}\times \frac{11}{12}\times \frac{11}{12}\times \frac{11}{12}\times 48$

$\inline \dpi{100} \fn_cm \frac{161051}{5184}$ = $\inline \dpi{100} \fn_cm 31\frac{347}{5184}$ liters

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459
Q:

In what proportion water must be added to spirit to gain 20% by selling it at the cost price ?

Answer

Let the C.P of spirit be = Rs.10 per litre

S.P of the mixture = Rs. 10 per litre

Profit = 20

$\inline \dpi{100} \fn_cm \therefore$ C.P of the mixture = Rs. $\inline \dpi{100} \fn_cm \frac{10\times 100}{120}$ = Rs. $\inline \dpi{100} \fn_cm \frac{25}{3}$ per litre

$\inline \dpi{100} \fn_cm \frac{Quantity\: of\: water}{Quantity\: of\: spirit}=\frac{5}{3}\times \frac{3}{25}=\frac{1}{5}$

$\inline \dpi{100} \fn_cm \therefore$Ratio of water and spirit = 1 : 5

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1204
Q:

A sum of Rs.118 was divided among 50 boys and girls such that each boy received Rs.2.60 and each girl Rs.1.80. Find the number of boys and girls ?

Answer

Average money received by each = $\inline \dpi{100} \fn_cm \frac{118}{50}$ = Rs. 2.36

$\inline \dpi{100} \fn_cm \therefore$Ratio of No.of boys and girls = 56 : 24 = 7 : 3

$\inline \dpi{100} \fn_cm \therefore$ Number of boys = $\inline \dpi{100} \fn_cm 50\times \frac{7}{10}$ = 35

Number of girls = 50 - 35 = 15

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863
Q:

A man travelled a distance of 80 km in 7 hours partly on foot at the rate of 8 km per hour and partly on bicycle at 16 km /hr. Find the distance travelled on foot ?

Answer

$\inline \dpi{100} \fn_cm \frac{Time\: taken\: on\: foot}{Time\: taken\: on\: bicycle}=\frac{32}{24}=\frac{4}{3}$

Thus out of 7 hrs in all, he took 4 hrs to travel on foot

$\inline \dpi{100} \fn_cm \therefore$ Distance covered on foot in 4 hrs = ( 4 x 8) = 32 km

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998
Q:

In what ratio should two varieties of tea at Rs. 60 per kg and Rs.120 per kg be mixed together so that by selling the mixture at Rs.96 per kg, a profit of Rs.20% is obtained ?

Answer

Let us first calculate the cost of price of the mixture. the selling price of the mixture is given as Rs.96 and the profit is given as 20%. So, Cost price = $\inline \dpi{100} \fn_cm 96\times \frac{100}{120}$ = Rs. 80

Now, let us apply allegation method :

= 40 : 20 =  2 : 1

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