AMO 2027 Grades 4-5 SET 15 - Self-study

Ten lampposts are equally spaced along a straight line. The distance between two adjacent lampposts is 20 m. What is the distance between the first and the last lamppost?

Mr. Know-Everthing has 4 times as many T-shirts as long sleeve shirts. He buys 28 more long sleeve shirts and gives away 18 T-shirts. The total number of T-shirts and long sleeve shirts he has becomes 310. How many T-shirts does he have now?

The sum of the digits of a two-digit number is 11. If we interchange the digits then the new number formed is 45 less than the original. Find the original number.

There is an equal number of cars and motorcycles in a parking lot. There are 426 wheels altogether. How many cars are there?

An octopus has 8 legs and goat has 4 legs. The total number of octopuses and goats in a zoo is 18, and their total legs is 96. How many goats are there in this zoo?

A bag contains some sweets that can be divided evenly among 3, 4 or 6 children with no remainder. What is the smallest possible number of sweets in the bag?

Jenny had 36 dollars. She spent $\frac{5}{12}$ of it. Her father gave her 20 dollars more. How much does she have now?

There are three ropes. The first ropes is 14m longer than the second rope. The second rope is 16m longer than the third one. If the total length of these three ropes is 190m, how long is each rope?

Answer entry: lengths in metres, in first;second;third order, separated by semicolons.

**Editorial input note:** Use no spaces before or after semicolons.

(a) A boat can travel with a speed of 13km/h in still water. If the speed of the stream is 4km/h, find the time taken by the boat to go 68km downstream.

(b) Speed of a boat in standing water is 11km/h and the speed of the stream is 1km/h. A man rows to a place at a distance of 240km and comes back to the starting point. Find the total time taken by him.

(c) If Anshul rows a boat 15km upstream and 21km downstream taking 3 hours each time, then find the speed of the stream.

Answer entry: (a) hours;(b) hours;(c) km/h, in that order, numbers only separated by semicolons.

**Editorial input note:** Use no spaces before or after semicolons.

The information below shows the number of students who visited the Science Centre. How many students are there?
(Each person symbol represents 2 students.)

Readable pictogram: classes 3A, 3B, 3C, 3D, 3E have respectively 6, 3, 8, 4, 10 full person symbols. Each symbol represents 2 students.



Answer entry: the total number of students across all five classes.

ABCD is a rectangle with area equal to 36 square units. Points E, F and G are midpoints of the sides on which they are located. How many square units are there in the area of triangle EFG?

Tom packs 8 kg of sugar into the same size packets. Each packet contains 900 grams of sugar. How much sugar is left unpacked?

Find the maximum number of trees which can be planted, 10 metres apart, on two sides of a straight road 150 metres long and 12 meters wide.

In the following cryptarithm, all letters stand for different digits. Find the sum (A + B + C + D).
$\overline{A8BC}-\overline{3D98}=2014$.

A typist used 1152 digits for book's page numbers. How many pages did the book have?