Question

the ratio of the number of pens to the number of pencils is 7:5. After 21 pens and 21 pencils were sold, the ratio becomes 11:7. how many pencils were left at the stall?​

Answer 1

Answer:

There are 77 pens and 49 pencils were left at the stall .

Step-by-step explanation:

Let there are p pens and q pencils were left in the stall

then , p/q = 11/7

⇒ 7p = 11q →(1)

before selling the 21 pen and 21 pencils the ratio of pen pencils is  $\frac{p+21}{q+21}$

according to question ,  $\frac{p+21}{q+21}$ = 7/5

⇒ 5p + 105 = 7q + 147

⇒ 5p - 7q = 42 →(2)

5×(1) ⇒ 35p = 55q → (3)

7×(2) ⇒ 35p - 49q = 294

⇒ 55q - 49q = 294 [ from (3) ]

⇒ 6q = 294

⇒ q = 49

Now , from (1) , 7p = 11×49

⇒ p = 77

Hence finally 77 pens and 49 pencils were left bin the stall