S K Gupta and Anubhuti Gangal Solutions for Chapter: Linear Equations in One Variable, Exercise 2: Exercise 13(B)

The sum of the digits of a two-digit number is $7$. The number obtained by interchanging the digits exceeds the original number by $27$. Find the number.

Ranjana's mother gave her $₹245$ for buying New Year cards. If she got some $10$ rupee cards, $\frac{2}{3}$ as many $5$ rupee cards, and $\frac{1}{5}$ as many $15$ rupee cards, how many of each kind did she buy?

The enrolment in school this year is $552$. This is an increase of $15\%$ over last year's enrolment. How many were enrolled last year?

A fruit vendor buys some oranges at the rate of $₹5$ per orange. He also buys an equal number of bananas at the rate of $₹2$ per banana. He makes a $20\%$ profit on oranges and a $15\%$ profit on bananas. at the end of the day, all the fruit is sold out. His total profit is $₹390$. Find the number of oranges purchased.

A two digit number becomes five-sixth of itself when its digits are reversed. The two digits differ by $1$. The number is

The ratio of the present ages of two brothers in $1:2$ and $5$ years back the ratio was $1:3$. What will be the ratio of their ages after $5$ years?

Two trains start from $P$ and $Q$ respectively and travel towards each other at a speed of $50 \mathrm{km}/\mathrm{hr}$ and $40 \mathrm{km}/\mathrm{hr}$ respectively. By the time they meet, the first train has travelled $100 \mathrm{km}$ more than the second. The distance between $P$ and $Q$ is

Nine persons went to a hotel for taking their meals. Eight of them spent $₹12$ each over their meals and the ninth spent $₹8$ more than the average expenditure of all the nine. What was the total money spent by them?