20
jewellellas gulu Vals UI Toldidan
to obtain a bar of 16 carats gold weighing 120 grams. [Given pure gold = 24 carats).
OR
Seven times a two digit number is equal to four times the number obtained by reversing the
places of its digits. If the difference between the digits is '3', find the number.
26] If the two zeros of the polynomial P(x) = x4 - 6x3 – 26x2 +138x – 35 are 2 + 3 and 2-13.
Find the other zeroes.
27] Two circles with centres 'X' and 'Y' of radii 9 cm and 2 cm touch the third circle with center
'Z' externally as shown in the figure. If xzy = 90°, find the radius of the circle with 'Z' as
center.
6
2 cm
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117 cm
OR
Find the roots of the equation (x2 + 3x)2 – (x2 + 3x) – 6 = 0.
7
T
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and
in that order divide a line seomentioining A (1.6) and B 5. -2) into
Answers
Answer: 80 grams of 18-carat gold and 40 grams of 12-carat gold
Solution:
Since pure gold is 24-carat,
Fractional purity of gold in 18-carat bar = 18/24
Fractional purity of gold in 12-carat bar = 12/24 and
Fractional purity required in the gold-bar to be made from above 2 bars = 16/24
If x grams be the quantity of 18-carat gold that is to be melted to obtain a 120 grams bar of 16-carat gold, then the quantity of 12-carat gold to be melted for the same purpose is (120-x) grams since total weight is given to be 120 grams. Now,
Fractional gold purity in the final bar
= [(fractional purity in 18-carat gold bar) (weight of 18-carat bar) + (fractional purity in 12-carat gold bar) (weight of 12-carat bar)] ÷ (Total weight of bar)
Substituting the values from above,
16/24 = [18/24 . x + 12/24 . (120 -x )] /120
Multiplying both sides by 24,
16 = [18 . x + 12 . (120 -x )] /120
Multiplying again both sides by 120,
16 . 120 = [18 . x + 12 . (120 -x )] = 18x + 12.120 - 12x
Simplify RHS and transpose the constant term from RHS to LHS to obtain,
(16–12)120 = 6x Or, 6x = 4 . 120
Or, x = 4.20 = 80 grams
Therefore, 120 - x = 120 - x = 120 - 80 = 40 grams