91Ó°ÊÓ

If the system of equations \(4 x+p y=21\) and \(p x-2 y=15\) has unique solution, then which of the following could be the value of \(p ?\) (a) 103 (b) 105 (c) 192 (d) 197 (1) Both (a) and (b) (2) Both (c) and (d) (3) (a), (b) and (d) (4) All of (a), (b), (c) and (d)

A mother said to her son, "the sum of our present ages is twice my age 12 years ago and nine years hence, the sum of our ages will be thrice my age 14 years ago". What is her son's present age? (in years) (1) 8 (2) 12 (3) 15 (4) 10

A told \(\mathrm{B}\), "when I was as old as you are now, then your age was four years less than half of my present age". If the sum of the present ages of \(\mathrm{A}\) and \(\mathrm{B}\) is 61 years, what is B's present age? (in years) (1) 9 (2) 25 (3) 43 (4) 36

A sum of Rs 400 was distributed among the students of a class. Each boy received \(\mathrm{Rs} 8\) and each girl received \(\mathrm{Rs} 4\). If each girl had received \(\mathrm{Rs} 10\), then each boy would have received \(\mathrm{Rs} 5\). Find the total number of students of the class. (1) 40 (2) 50 (3) 60 (4) 70

The sum of the speeds of a boat in still water and the speed the current is \(10 \mathrm{kmph}\). If the boat takes \(40 \%\) of the time to travel downstream when compared to that upstream, then find the difference of the speeds of the boat when travelling upstream and down stream. (1) \(3 \mathrm{kmph}\) (2) \(6 \mathrm{kmph}\) (3) \(4 \mathrm{kmph}\) (4) \(5 \mathrm{kmph}\)

A two-digit number is formed by either subtracting 17 from nine times the sum of the digits or by adding 21 to 13 times the difference of the digits. Find the number. (1) 37 (2) 73 (3) 71 (4) Cannot be determined

Swathi starts her job with certain monthly salary and earns a fixed increment every year. If her salary was Rs 22500 per month after 6 years of service and Rs 30000 per month after 11 years of service. Find her salary after 8 years of service (in \(\mathrm{Rs}\) ). (1) 24000 (2) 25500 (3) 26000 (4) 24500

A three digit number abc is 459 more than the sum of its digits. What is the sum of the 2 digit number ab and the 1-digit number a? (1) 71 (2) 61 (3) 51 (4) Cannot be determined

The total cost of 6 erasers and 9 pens is at least Rs 102 and the cost of each eraser is at most Rs 5. Find the minimum possible cost (in rupees) of a pen. The following are the steps involved in solving the above problem. Arrange them in sequential order. (a) Let the cost of each eraser be \(\mathrm{Rs} \mathrm{x}\) and cost of each pen be \(\mathrm{Rs} \mathrm{y}\). (b) \(6 x+9 y \geq 102\) and \(y \leq 5\). (c) \(6 \times 5+9 \mathrm{y} \geq 102 \Rightarrow 9 \mathrm{y} \geq 72 \Rightarrow \mathrm{y} \geq 8\) (d) The minimum possible cost of a pen is \(\operatorname{Rs} 8\). (1) abdc (2) abcd (3) \(\mathrm{dabc}\) (4) acbd

Ramesh had a total of 30 coins in his purse of denominations \(\mathrm{Rs} 5\) and \(\mathrm{Rs} 2\). If the total amount with him is Rs 120, then find the number of \(\mathrm{Rs} 5\) coins. (1) 20 (2) 10 (3) 4 (4) 12