Exercise : 8


1. How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may, on selling the mixture at 40 paise per kg gain 25% on the outlay?
(a) 15 kg
(b) 18 kg
(c) 20 kg
(d) 24 kg
(e) None of these
Ans.c

Here, cost price of mixture = \(100 \times \frac{100}{100 + 25}\) = 32 paise

\(\therefore \frac{q_{1}}{q_{2}} = \frac{32 - 24}{42 - 32} = \frac{8}{10} = \frac{4}{5}\)

and hence q1 = 45 × 25 = 20 kg

2. A trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg. In order to earn a profit of 25%, what should be the sale price of the mixed tea?
(a) 23.75
(b) 22
(c) 20
(d) 19.20
(e) None of these
Ans.c

C.P. of mixture = \(\frac{80 \times 15 + 20 \times 20}{80 + 20} = 16\)

∴ S.P. = \(\frac{\left(100 + 25 \right)}{100} \times 16 = 20\)

3. A company blends two varieties of tea from two different tea gardens, one variety costing 20 per kg and other 25 per kg, in the ratio 5 : 4. He sells the blended tea at 23 per kg. Find his profit percent :
(a) 5% profit
(b) 3.5% loss
(c) 3.5% profit
(d) No profit, no loss
(e) None of these
Ans.c

Let the quantity of two varieties of tea be 5x kg and 4x kg, respectively.

Now, SP = 23 × 9x = 207x

and CP = 20 × 5x + 25 × 4x = 200x

Profit % = \(\frac{7x}{200x} \times 100 = 3.5 \%\)

4. Alcohol cost 3.50 per litre and kerosene oil cost 2.50 per litre. In what proportion these should be mixed so that the resulting mixture may be 2.75 per litre?
(a) 2 : 5
(b) 1 : 3
(c) 4 : 7
(d) 2 : 3
(e) None of these
Ans.b

By the rule of alligation, we have

6

∴ Required ratio = 0.250.75 = 13 i.e, 1 : 3

5. Pure milk costs 3.60 per litre. A milkman adds water to 25 litres of pure milk and sells the mixture at 3 per litre. How many litres of water does he add?
(a) 2 litres
(b) 5 litres
(c) 7 litres
(d) 11 litres
(e) None of these
Ans.b

In mixture,

\(\frac{Quantity \; of \; pure \; milk}{Quantity \; of \; water} = \frac{3 - 0}{3.6 - 3} = \frac{3}{0.6} = \frac{5}{1}\)

Since in every 5 litres of milk, he adds 1 litre of water.

∴ In every 25 litres of milk, he adds 5 litres of water.