Question
In an envelope there are some ₹5 notes and some ₹10 notes. Total amount of these notes together is ₹350. Number of ₹5 notes are less by 10 than twice the number of ₹10 notes. Then find the number of ₹5 and ₹10 notes.
✓
Answer
Let the number of ₹5 notes be ‘x’ and the number of ₹10 notes be ‘y’
Total amount of x notes of ₹ 5 = ₹ 5x
Total amount ofy notes of ₹ 10 = ₹ 10y
∴ Total amount = 5x + 10y
According to the first condition,
total amount of the notes together is ₹350.
∴ 5x + 10y = 350 …(i)
According to the second condition,
Number of ₹ 5 notes are less by 10 than twice the number of ₹ 10 notes.
∴ x = 2y – 10
∴ x – 2y = -10 …..(ii)
Multiplying equation (ii) by 5,
5x – 10y = -50 …(iii)
Adding equations (i) and (iii),
5x + 10y =350
+ 5x – 10y = -50
10x =300
$\therefore x=\frac{300}{10}$
$\therefore x=30$
Substituting $x=30$ in equation (ii),
$x-2 y=-10$
$30-2 y=-10$
$\therefore 30+10=2 y$
$\therefore 40=2 y$
$\therefore y=\frac{40}{2}$
$\therefore y=20$
There are 30 notes of $₹ 5$ and 20 notes of $₹ 10$ in the envelope.
Total amount of x notes of ₹ 5 = ₹ 5x
Total amount ofy notes of ₹ 10 = ₹ 10y
∴ Total amount = 5x + 10y
According to the first condition,
total amount of the notes together is ₹350.
∴ 5x + 10y = 350 …(i)
According to the second condition,
Number of ₹ 5 notes are less by 10 than twice the number of ₹ 10 notes.
∴ x = 2y – 10
∴ x – 2y = -10 …..(ii)
Multiplying equation (ii) by 5,
5x – 10y = -50 …(iii)
Adding equations (i) and (iii),
5x + 10y =350
+ 5x – 10y = -50
10x =300
$\therefore x=\frac{300}{10}$
$\therefore x=30$
Substituting $x=30$ in equation (ii),
$x-2 y=-10$
$30-2 y=-10$
$\therefore 30+10=2 y$
$\therefore 40=2 y$
$\therefore y=\frac{40}{2}$
$\therefore y=20$
There are 30 notes of $₹ 5$ and 20 notes of $₹ 10$ in the envelope.
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