9. Gold is 19 times as heavy as water and copper 9 times as heavy as water. The ratio in which these two metals be mixed so that the mixture is 15 times as heavy as water is:
a. 1 : 2
b. 2 : 3
c. 3 : 2
d. 19: 135

Answer: C

Explanation:
This question can be solved using weighted average formula. If two quantities of weights m, n have concentrations x, y are mixed then, final concentration = $\dfrac{{mx + ny}}{{m + n}}$
Take 1 unit of gold and x units of copper.
$\displaystyle\frac{{1 \times 19 + x \times 9}}{{1 + x}} = 15 \Rightarrow 19 + 9x = 15 + 15x$
$ \Rightarrow x = \displaystyle\frac{2}{3}$
So they are to be mixed in the ratio 1 : x = $1:\displaystyle\frac{2}{3}$ or 3 : 2

10. If a:b=c:d, then $\displaystyle\frac{{ma + nc}}{{mb + nd}}$ is equal to
a. m : n
b. na:mb
c. a : b
d. md:nc

Answer: C

Explanation:
Let $\displaystyle\frac{a}{b} = \displaystyle\frac{c}{d} = k$. Then a = bk and c=dk
$\displaystyle\frac{{ma + nc}}{{mb + nd}} = \displaystyle\frac{{mbk + ndk}}{{mb + nd}} = k\left[ {\displaystyle\frac{{mb + nd}}{{mb + nd}}} \right]$ = k
But $k = \displaystyle\frac{a}{b}$ So the required ratio = a : b

11. Rs.1050 is divided among P, Q and R. The share of P is $\displaystyle\frac{2}{5}$ of the combined share of Q and R. Thus, P gets:
a. Rs.200
b. Rs.300
c. Rs.320
d. Rs.420

Answer: B

Explanation:
Let Q + R got 5 units then P gets 2 units.
P : (Q + R)= 2:5
But total P + Q + R = 7 units. So,
P's share =Rs.$\left( {1050 \times \displaystyle\frac{2}{7}} \right)$=Rs.300

12. Divided Rs.600 among A,B and C so that Rs.40 more than $\displaystyle\frac{2}{5}$th of A's share. Rs.20 more than $\displaystyle\frac{2}{7}$ of B's share and Rs.10 more than $\displaystyle\frac{9}{{17}}$th of C's share may all be equal. What is A's share ?
a. Rs.280
b. Rs.150
c. Rs.170
d. Rs.200

13. 729 ml.of a mixture contains milk and water in the ratio of 7:2. How much more water is to be added to get a new mixture containing milk and water in the ratio of 7:3 ?
a. 60 ml
b. 70 ml
c. 81 ml
d. 90 ml

14. A and B are two alloys of gold and copper prepared by mixing metals in proportions 7:2 and 7:11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the proportion of gold and copper in C will be :
a. 5 : 9
b. 5 : 7
c. 7 : 5
d. 9 : 5

Answer: C

Explanation:
Gold in C = $\left( {\displaystyle\frac{7}{9} + \displaystyle\frac{7}{{18}}} \right) = \displaystyle\frac{{21}}{{18}} = \displaystyle\frac{7}{6}$
Copper in C = $\left( {\displaystyle\frac{2}{9} + \displaystyle\frac{{11}}{{18}}} \right) = \displaystyle\frac{{15}}{{18}} = \displaystyle\frac{5}{6}$
Gold : Copper = $\displaystyle\frac{7}{6}:\displaystyle\frac{5}{6} = 7:5$

15. The students in three classes are in the ratio 2:3:5. If 20 students are increased in each class, the ratio changes to 4:5:7. The total number of students before the increase were :
a. 10
b. 90
c. 100
d. None of these

Answer: C

Explanation:
Let the number of students be 2x, 3x and 5x.
Then (2x + 20) : (3x + 20):(5x + 20)
= 4 : 5 : 7
So, $\displaystyle\frac{{2x + 20}}{4} = \displaystyle\frac{{3x + 20}}{5} = \displaystyle\frac{{5x + 20}}{7}$
5(2x + 20)=4(3x + 20) or x = 10
Hence, total number of students before increase =10x = 100

16. The ratio of money with Ram and Gopal is 7:17 and that with Gopal and Krishna is 7:17 . If Ram has Rs.490, Krishna has :
a. Rs.2890
b. Rs.2330
c. Rs.1190
d. Rs.2680