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Examples

June 4, 2020
Category: Examples

(1) In what proportion must rice at Rs. 12.50 per kg. be mixed with rice at Rs. 15.20 per kg., so that the mixture be worth Rs. 14.00 per kg. ?

Solution.

$\therefore$ They must be mixed in the ratio 1.20 : 1.50 = 4 : 5.

(2) How many kilograms of sugar costing Rs. 10.50 per kg. must be mixed with 80 kg. of sugar costing Rs. 15.00 per kg. so that 10 % may be gained by selling the mixture at Rs. 13.20 per kg ?

Solution.

$\frac{13.20 \times 100}{110}= \textup{Rs.}12$

They must be mixed in the ratio 3 : 1.50 = 2 : 1.

$\frac{80 \times 1}{2}$ = 40 kg

(3) In what proportion must water be mixed with milk to gain 20 % by selling it at cost price ?

Soln. Gain = 20 % ( Due to water )

water milk

20 100

$\therefore$ Water : Milk = 20 : 100 = 1 : 5

(4) In what ratio must a person mix three kinds of wheat costing him Rs. 10.20, Rs. 10.45 and Rs. 10.70 per kg., so that the mixture may be worth Rs. 10.50 per kg. ?

Solution.

They must be mixed in the ratio 0.20 : 0.20 : 0.35 = 4 : 4 : 7

(5) A butler stole wine from a butt of sherry which contained 80 % of spirit and he replaced, what he had stolen by wine containing only 32 % spirit. The butt was then of 48 % strength only. How much of the butt did he steal ?

Solution.

They must be mixed in the ratio 16 : 32 = 1 : 2.

Thus, $\frac{1}{3}$ of the butt of sherry was left and hence the butler drew out $\frac{2}{3}$ of the butt.

(6) The average weekly salary per head of the entire staff of a factory consisting of supervisors and the labourers is Rs. 5000. The average salary per head of the supervisors is Rs. 20000 and that of the labourers is Rs. 2000. Given that the number of supervisors is 10, find the number of labourers in the factory.

Solution.

Thus, the ratio of supervisors to labourers = 3000 : 15000 = 1 : 5

$\frac{10 \times 5}{1} = 50 \textup{ Lavbourers}$

(7) A man possessing Rs. 15000 lent a part of it at 5 % simple interest and the remaining at 8 % simple interest. His total income after 2 $\frac{1}{2}$ years was Rs. 2550. Find the sum lent at different rates.

Solution.

Thus, the ratio of amount at 5 % to 8 % = 450 : 675 = 2 : 3

$\therefore$ Money lent at 5 % = Rs. $\left (15000\times\frac{2}{5} \right )$ = Rs. 6000

$\therefore$ Money lent at 8 % = Rs. 15000 – Rs. 6000 = Rs. 9000

(8) A man traveled a distance of 300 km. in 30 hours, partly on foot at the rate of 8 km. per hour and partly on bicycle at 20 km. per hour. Find the distance traveled on foot.

Solution.

Average distance traveled in 1 hr. = $\frac{300}{30}$ = 10 km.

Average distance traveled on foot = $\frac{8}{1}$ = 8 km. & on bicycle = $\frac{20}{1}$ = 20 km.

Thus, time taken on foot to on bicycle = 10 : 2 = 5 : 1

Total time taken on foot = $\frac{5}{6}\times$ 30 = 25 hrs.

Distance covered on foot in 8 hours = ( 8 $\times$ 25 ) km = 200 km.

(9) A sum of Rs. 84 was divided among 120 boys and girls. Each boy gets 50 paise and a girl 80 paise. Find the number of boys and girls.

Solution.

Average money received by each student = $\frac{8400}{120}$ = 70 P.

Thus, no. of boys to no. of girls = 10 : 20 = 1 : 2

$\therefore$ No. of boys = $\frac{1}{3}\times$ 120 = 40 & no. of girls = 120 – 40 = 80

(10) A lump of two metals weighing 24 gms. is worth Rs. 420 but if their weights be interchanged, it would be worth Rs. 180. If the price of one metal be Rs. 5.00 per gm., find the weight of the other metal in the mixture.

Solution.

Weight of 1^st Metal Weight of 2^nd Metal Cost

(in gm.) (in gm.)

Originally x + 24 -x = Rs. 420
(24 gm)