  Question

(i) In a mixture of 45 litres, the ratio of milk to water is 13: 2. How much water must be added to this mixture to make the ratio of milk to water as 3: 1?(ii) The ratio of the number of boys to the numbers of girls in a school of 560 pupils is 5: 3. If 10 new boys are admitted, find how many new girls may be admitted so that the ratio of the number of boys to the number of girls may change to 3: 2.

Solution

(i) It is given thatMixture of milk to water $$= 45\ litres$$Ratio of milk to water $$= 13: 2$$Sum of ratio $$= 13 + 2 = 15$$Here the quantity of milk $$= (45 \times 13)/ 15 = 39\ litres$$Quantity of water $$= 45 \times 2/15 = 6\ litres$$Consider x litre of water to be added, then water $$= (6 + x)\ litres$$Here the new ratio $$= 3: 1$$$$39: (6 + x) = 3: 1$$We can write it as$$\dfrac{39}{ (6 + x)} =\dfrac{ 3}{1}$$By cross multiplication$$39 = 18 + 3x$$$$3x = 39 – 18 = 21$$$$x = 21/3 = 7\ litres$$Hence, $$7\ litres$$ of water is to be added to the mixture.(ii) It is given thatRatio between boys and girls $$= 5: 3$$Number of pupils $$= 560$$So the sum of ratios $$= 5 + 3 = 8$$We know thatNumber of boys $$= \dfrac{5}{8} \times 560 = 350$$Number of girls $$= \dfrac{3}{8} \times 560 = 210$$Number of new boys admitted $$= 10$$So the total number of boys $$= 350 + 10 = 360$$Consider x as the number of girls admittedTotal number of girls $$= 210 + x$$Based on the condition$$360: 210 + x = 3: 2$$We can write it as$$\dfrac{360}{ 210 + x} = \dfrac{3}{2}$$By cross multiplication$$630 + 3x = 720$$$$3x = 720 – 630 = 90$$So we get$$x = 90/3 = 30$$Hence, $$30$$ new girls are to be admitted.Maths

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