S Purkayastha Solutions for Chapter: Problem Solving, Exercise 1: Check Point

Entry ticket for an exhibition for a child is $₹ 6$ for and an adult is $₹ 10$. If a family spends $₹ 58$ for tickets. How many children and adults are there in that family $?$

A motorboat goes downstream in a river and covers the distance between two coastal towns in five hours. It covers this distance upstream in six hours. If the speed of the stream is $2 \mathrm{km}/\mathrm{h}$, find the speed of the boat in still water.

Can you think of a two-digit number such that the sum of the number obtained by reversing the order of digits is $165$ and the digits differ by $3$

Students of a class are made to stand in rows. If $3$ students are extra in a row, there would be $1$ row less. If $3$ students are less in a row, there would be $2$ more rows. Find the number of students in the class.

In a competitive examination, one mark is awarded for every correct answer and $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered $120$ question and got $90$ marks. How many questions did she answer correctly?

Chethan is reading a book which has $303$ pages. How many times does the digit $3$ gets printed in the page numbers? How many pages are there which have only one $3$ present?

How many $3$-digit even numbers can be formed from the digits $1,2,\mathrm{3,4},5,6$ if the digits can be repeated?

Sajda spends $₹878$ to buy pens and notebooks. Each notebook costs $₹41$ and each pen costs $₹39$. If she bought a total of $22$ items, how many notebooks and how many pens did she buy?