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Equations 1/4

19. In an examination, three marks will be awarded for every correct answer and one mark will be deducted for every wrong answer. A student attempted 70 questions and scored 170 marks. Find the number of questions he answered correctly.
a. 55
b. 58
c. 60
d. 65


20. If 3 is added to the denominator of a fraction, it becomes $\displaystyle\frac{1}{3}$ and if 4 be added to its numerator, it becomes $\displaystyle\frac{3}{4}$ ; the fraction is :
a. $\displaystyle\frac{4}{9}$
b. $\displaystyle\frac{3}{{20}}$
c. $\displaystyle\frac{7}{{24}}$
d. $\displaystyle\frac{5}{{12}}$


21. Of the three numbers, the first is twice the second and is half of the third. If the average of three numbers is 56, then the smallest number is
a. 24
b. 36
c. 40
d. 48


22. The difference of two numbers is 8 and ${\left( {\dfrac{1}{{12}}} \right)^{th}}$ of the sum is 1. The numbers are
a. 10, 2
b. 18, 26
c. 10, 18
d. 26, 34


23. A number is 25 more than its ${\left( {\frac{2}{5}} \right)^{th}}$. The number is
a. 60
b. 80
c. $\displaystyle\frac{{125}}{3}$
d. $\displaystyle\frac{{125}}{7}$


24. The sum of three numbers is 68. If the ratio between first and second be 2 : 3 and that between second and third be 5 : 3, then the second number is
a. 30
b. 20
c. 58
d. 48


25. The sum of two numbers is 100 and their difference is 37. The difference of their squares is
a. 37
b. 100
c. 63
d. 3700